From 7a233379383b6d2b2f4da8f6d61043a212a003f7 Mon Sep 17 00:00:00 2001 From: Jay Gambetta Date: Sun, 15 Apr 2018 17:36:21 -0400 Subject: [PATCH] redoing the reference/tools section (#119) Section one --- .gitignore | 5 +- CODEOWNERS | 3 + index.ipynb | 4 +- reference/tools/getting_started.ipynb | 338 +-- .../quantum_gates_and_linear_algebra.ipynb | 2651 +++++++++++++---- .../tools/visualizing_quantum_state.ipynb | 419 ++- reference/tools/working_with_backends.ipynb | 218 +- 7 files changed, 2632 insertions(+), 1006 deletions(-) create mode 100644 CODEOWNERS diff --git a/.gitignore b/.gitignore index be5e06560..c059c890e 100644 --- a/.gitignore +++ b/.gitignore @@ -11,6 +11,5 @@ Qconfig.py __pycache__/ -reference/tools/.ipynb_checkpoints/getting_started-checkpoint.ipynb - -reference/tools/.ipynb_checkpoints/working_with_backends-checkpoint.ipynb +reference/tools/.ipynb_checkpoints/* +reference/qis/.ipynb_checkpoints/* diff --git a/CODEOWNERS b/CODEOWNERS new file mode 100644 index 000000000..efa13fe58 --- /dev/null +++ b/CODEOWNERS @@ -0,0 +1,3 @@ +# Where component owners are known, add them here. + +reference/tools/* @jaygambetta \ No newline at end of file diff --git a/index.ipynb b/index.ipynb index 3159b84df..3db1edb26 100644 --- a/index.ipynb +++ b/index.ipynb @@ -32,9 +32,9 @@ "#### 2.1 [Getting started with QISKit](reference/tools)\n", "In this first topic, we introduce you to the basic features of QISKit. More tutorials covering QISKit features can be found in [here](#appendix_tools) and developer documentation can be found [here](https://www.qiskit.org/documentation/).\n", " * [Write and run your first quantum program](reference/tools/getting_started.ipynb) - how to use QISKit.\n", - " * [Working with different backends](reference/tools/working_with_backends.ipynb) - running a quantum program on different backends.\n", " * [Using different gates](reference/tools/quantum_gates_and_linear_algebra.ipynb) - list of gates in QISKit and their linear algebra.\n", - " * [Visualisation of quantum states](reference/tools/visualizing_quantum_state.ipynb) - illustrates the different tools we have for visualizing a quantum state.\n", + " * [Visualisation of quantum data and states](reference/tools/visualizing_quantum_state.ipynb) - illustrates the different tools we have for visualizing a quantum state.\n", + " * [Working with different backends](reference/tools/working_with_backends.ipynb) - Compiling and running a quantum program on different backends.\n", " \n", "#### 2.2 [Introduction to quantum information science](reference/qis)\n", "The next set of notebooks shows how you can explore some simple concepts of quantum information science. More tutorials on other quantum information science concepts can be found [here](#appendix_qis)\n", diff --git a/reference/tools/getting_started.ipynb b/reference/tools/getting_started.ipynb index 415f0ce3b..a766a73b0 100644 --- a/reference/tools/getting_started.ipynb +++ b/reference/tools/getting_started.ipynb @@ -26,9 +26,9 @@ "source": [ "## QISKit (Quantum Information Software developer Kit)\n", "\n", - "This tutorial aims to explain how to use QISKit. We assume you have installed QISKit if not please look at [qiskit.org](http://www.qiskit.org) or the install [documentation](../INSTALL.md). \n", + "This tutorial aims to explain how to use QISKit. We assume you have installed QISKit if not please look at [qiskit.org](http://www.qiskit.org) or the install [documentation](https://github.com/QISKit/qiskit-tutorial/blob/master/INSTALL.md). \n", "\n", - "QISKit is a Python software development kit that you can use to create your quantum computing programs based on circuits defined through the [OpenQASM 2.0](https://github.com/QISKit/qiskit-openqasm) specification, compile them, and execute them on several backends (real quantum processors online, simulators online, and simulators on local). For the online backends conects to the [IBM Q experience project](http://quantumexperience.ng.bluemix.net/).\n", + "QISKit is a Python software development kit that you can use to create your quantum computing programs based on circuits defined through the [OpenQASM](https://github.com/QISKit/qiskit-openqasm) specification and execute them on several backends (real quantum processors online, simulators online, and simulators on local). For the online backends conects to the [IBM Q Experience project](http://quantumexperience.ng.bluemix.net/).\n", "\n", "In addition to this tutorial, we have other tutorials that introduce you to more complex concepts directly related to quantum computing.\n", "\n", @@ -36,22 +36,9 @@ "- Familiarize yourself with the important concepts of [superposition and entanglement](../qis/superposition_and_entanglement.ipynb)." ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Basic Concept\n", - "\n", - "The basic concept of our quantum program is an array of quantum circuits. The program workflow consists of three stages: [Build](#sectionB), [Compile](#sectionC), and [Run](#sectionR). Build allows you to make different quantum circuits that represent the problem you are solving; Compile allows you to rewrite them to run on different backends (simulators/real chips of different [quantum volumes](http://ibm.biz/qiskit-quantum-volume), sizes, fidelity, etc); and Run launches the jobs.  After the jobs have been run, the data is collected. There are methods for putting this data together, depending on the program. This either gives you the answer you wanted, or allows you to make a better program for the next instance.\n", - "\n", - "### Building your program: Create it \n", - "\n", - "First you need to import the QuantumProgram package from QISKit." - ] - }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -60,20 +47,40 @@ "if sys.version_info < (3,5):\n", " raise Exception('Please use Python version 3.5 or greater.')\n", " \n", - "import qiskit\n", - "\n", "try:\n", " sys.path.append(\"../../\") # go to parent dir\n", " import Qconfig\n", " qx_config = {\n", " \"APItoken\": Qconfig.APItoken,\n", - " \"url\": Qconfig.url}\n", + " \"url\": Qconfig.config['url']}\n", "except:\n", " qx_config = {\n", " \"APItoken\":\"YOUR_TOKEN_HERE\",\n", " \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}" ] }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n", + "from qiskit import QuantumProgram\n", + "from qiskit.backends import discover_local_backends, discover_remote_backends" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Basic Concept\n", + "\n", + "The basic concept of our QISKit core is an array of quantum circuits. The workflow consists of three stages: [Build](#sectionB), [Compile](#sectionC), and [Run](#sectionR). Build allows you to make different quantum circuits that represent the problem you are solving; Compile allows you to rewrite them to run on different backends (simulators/real chips of different [quantum volumes](http://ibm.biz/qiskit-quantum-volume), sizes, fidelity, etc); and Run launches the jobs.  After the jobs have been run, the data is collected. There are methods for putting this data together, depending on the program. This either gives you the answer you wanted, or allows you to make a better program for the next instance.\n", + "\n", + "### Building your circuit: Create it " + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -83,40 +90,39 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Create a Quantum Register called \"q\" with 3 qubits\n", - "qr = qiskit.QuantumRegister(\"q\", 3)\n", + "qr = QuantumRegister(\"q\", 3)\n", "\n", "# Create a Classical Register called \"c\" with 3 bits\n", - "cr = qiskit.ClassicalRegister(\"c\", 3)\n", + "cr = ClassicalRegister(\"c\", 3)\n", "\n", "# Create a Quantum Circuit called involving \"qr\" and \"cr\"\n", - "circuit = qiskit.QuantumCircuit(qr, cr)" + "circuit = QuantumCircuit(qr, cr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Building your program: Add Gates to your Circuit\n", "After you create the circuit with its registers, you can add gates to manipulate the registers. As you proceed though the tutorial you will find more quantum gates and circuits but the below is an example of the quantum half adder." ] }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 82, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -129,7 +135,9 @@ "circuit.x(qr[1])\n", "\n", "# Barrier to seperator the input from the circuit\n", - "circuit.barrier(qr)\n", + "circuit.barrier(qr[0])\n", + "circuit.barrier(qr[1])\n", + "circuit.barrier(qr[2])\n", "\n", "# Toffoli gate from qubit 0,1 to qubit 2\n", "circuit.ccx(qr[0], qr[1], qr[2])\n", @@ -152,7 +160,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -165,7 +173,9 @@ "creg c[3];\n", "x q[0];\n", "x q[1];\n", - "barrier q[0],q[1],q[2];\n", + "barrier q[0];\n", + "barrier q[1];\n", + "barrier q[2];\n", "ccx q[0],q[1],q[2];\n", "cx q[0],q[1];\n", "measure q[0] -> c[0];\n", @@ -196,19 +206,19 @@ }, { "cell_type": "code", - "execution_count": 84, + "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "data": { - "image/png": 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+ "image/png": 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bgMjIyFmzZg0cOFCAGETm9evXixcvZjKZqqqqd+7c6TXaTZs2YQfp6elYjz8QvcLCwvj4+NOnT2/evBmvOnHZu0dKSurEiRN79+7lssU2AHwRJIljV+LS0tId56w7OTnJyspGRUV1HBV79OhRhJCLi0vXSl68eJGTkyPmw8Ozs7Nnz57d3NxMoVDi4uKMjY17PcXU1JSzFG1wcPD3uqWkmDM0NKTRaJxbFMIrKys7fPjwqlWrsG35hLR58+bIyEjh6wEACZDE2Wx2WloaQmjcuHFycnKcx5WUlDZu3FhUVLRo0aL8/Hxsnejw8PBRo0Z1uzprZGTkwIEDnZ2dhYm+rxkZGWHDb+h0Ou9LmnCGXWZmZsLG50TB950PDg6mUChBQUE41gkALvjuK8zOzm5oaED/t2RKR8HBwTU1NREREQkJCdgjY8eOvXnzZsdcj6HRaDExMX5+frh0VgLQ18zMzOzt7fldngUAEeA7h3bbIY6RkpI6fvy4v79/YmIijUYzMzNzcnLq9oIoNjYW31+7APSp1atXEx0CAN3jO4l7eHgsWLAAIdT1+hpjbGzca99xVFSUtbU1L13MAAAAuJDW1dXtdSPEjigUCr+rBXVVXl4eEhIiZCUAAACksQEkIvb582fRNwoAAN8fGDsBAAASDJI4AABIMEjiAAAgwfr7MO2rV6/m5OQQHQVCCNXV1SGEGhsbiQ4EACBJ+nUS19DQKCoq+vLlC9GBIIQQi8WSl5fnLO0L+IV9CwYHB+O7f/m///6rrq6OrZmDbSGro6ODY/3Yx4+vLdxoNNqCBQtGjx4tcXvSv3//ftOmTTY2NkQH8l3p10nczc1NVVW11818RYPFYqWlpXF2UwL8UlBQoFAoZ8+exbfa+vp6CoWCLV2JDcZVVFTEsX42m02hUPiqMzU1NTEx8dWrVxI34bm2tnbIkCGQxPElYR8CfJ08eVJOTq6nWUsixmKx6uvr7e3tV61aRXQsEsnPz4+z9RKODAwMHB0djx8/jhBydnZmMBiJiYm4t8IXbO3+GzduCLwoLlGkpaWxNasBjvp1EkcI7dq1a/369URHgRBCnz59MjIywmXvAgBA/wGjUwAAQIJBEgcAAAlGZjAYdDpdxK1iuycDAAAQEtnPz6/bTRv6lI6OTkREhIgbBQD0hatXr27fvp3oKPovcmVlZWVlpYhbHT9+/LFjx0TcKAAAd3V1dX5+fp8+fSI6kP6LmD5xb2/v7OzsTrsqAwAkzp49exoaGnbu3El0IP0XMUncxcVFQ0MD9ortP5qbm7Ozs9+/f48QSk1NLSgoEP2dGIC7wsLCY8eO+fv7GxoaEh1L/0VMEpeRkVmyZMmVK1eam5sJCQCIRlVV1dGjR3/88UcVFRVjY2NsJ5D58+fr6elpaGi4ublduHCBrxnnQKxs2bKFSqUGBgYSHUi/RtgQQx8fn4aGhmvXrhEVgGDq6uqqqqqqqqqqq6t5Kd/a2lr1f/o6NrHS2NgYHBxsYGCwbt269vb20NDQhISEffv2IYRu3rx58+bNX3/99d9//126dOnIkSOjoqKYTCbRIQP+vH379sqVK9u2bYMFf4hFWBI3NTU1NzePiooiKgDBxMTEDBo0aNCgQdra2gUFBdwLNzc329raYuVxX9NDnKWmphobG+/du3fp0qUlJSXPnj1bv379rFmzsKWjzM3NXVxcdu/enZmZmZ6ePm7cOB8fn2nTpon+BjsQxoYNG3R0dPz9/YkOpL8jcrKPj49PUlJSr6lQrHh7e+vq6iKEGAwGdl3ZEyaT6e7u/ubNG4TQmjVrNm7cKKIQiRYTE/PDDz9oaGh8+PAhIiJCW1ubS2FTU9Pbt2/fu3cvJydn4sSJ7969E1mcQBhxcXHJycmhoaH4rhkJBEBkEvf09JSRkTlz5gyBMfCLQqEEBQVhx1FRUeXl5T2V9Pf3v3XrFkJo8eLFhw4dElF8RLt3756np+eMGTNevHgxatQoHs9ycHB4+/atsrKyg4NDYWFhXwYIcNDe3r5lyxZLS0s3NzeiYwGEJnF1dXVXV9czZ86wWCwCw+DX0qVLsXvxbW1tBw4c6LZMSEjIqVOnEEJ2dnbnzp0jkUgiDZEgnz598vDwmDx5cmxsLL/rterp6T148EBGRsbFxQVb8RWIrYiIiJycnAMHDvSTD7aYI3jtFG9v7+Li4sePHxMbBl+kpKSCg4Ox41OnTnW9w3n27Nnff/8dIWRmZnb9+nVxWLlfNF+TPj4+qqqqAr/kwYMH37hxIycnZ8eOHbjHBvBSV1cXEhLi5uY2depUomMBCPGexNlsdmJiopeX16RJk+zt7bdu3VpRUYEQ2rBhg7Gx8ejRowVbDmXmzJlDhw6VuNubHh4eJiYmCKHm5uZOXSX379/39fVFCOnq6t69e1dZWZmYEBFCCFVWVm7atMnIyAj7e/Pw8Fi/fn1ZWVlftBUXF/fy5ctDhw4JM1ZhwoQJAQEBR48ezc/PxzE2gCNsds/u3buJDgT8n9mzZ9va2rK5Ki0ttbW17XSiiorKkydPsH7PsWPHcq+Bi61bt8rJydXW1gpcg8BIJNKBAwcEOzcmJobzPtTV1WEPpqWlYd0IWlpaOTk5fFWYnZ2NEEpISBAsnq6uXLmioKDQ9X+cSqWeO3cOr1Y4TE1NJ0+ezGKxuJTB3rTi4mIuZb59+6ampvbzzz/jHaCA9PX1/f39sWMnJ6cZM2YQGw+bzcZu/z569Ej0TRcUFMjJya1du1aw06WkpPbt24dvSKD3K/G8vLyJEycmJSUhhOTl5T09PUNCQnx9fWk02rx587BdhidNmiTwt4i3t3dra2t0dLTANRBi4cKFpqamCKH6+nps25fCwsJZs2bRaDQFBYXbt28TO4ctJibG3d29qamp61MtLS1eXl7nzp3DsbnPnz9nZGT4+/sL30mqrq7u6el5/fp1GDkuhmB2jxjqJYljG4ZhPSfTpk3Ly8u7ePFiYGDgX3/9df78eewKFCFkaWnZ6UQmk8nj7SkDA4Np06ZJ3BR8EonE6bo9dOhQcXGxo6NjZWWltLT01atXJ06cSGBsVVVVy5cvx/5rerJq1Soc+1Xi4uIoFIqTkxMutbm6un758uXVq1e41AbwArN7xFMvSXzNmjXYkK/ly5c/fvx40KBBnKfc3d319PSw405X4oWFhdOnTz99+jSPQfj4+KSkpGRmZvIetzhwdXW1sLBACH379s3MzAxbyO3vv/92dHQkNrDDhw/3+g3a0tJy8OBBvFp8/fr1hAkT1NTUcKnN1tZWRkYGkri4gdk94olbEn///j02z9DQ0DA8PLzT1tokEsnAwAAhRKVSR48ejRC6cuVKQECAnZ2dvr5+cnIy70G4ubkpKipK3O1NhBBn8bba2lqEUFhYmOgXZ+8KG5/eq/j4eLxaLC8vHz58OF61USiUQYMGcRmDD0QPm90TFhYGs3vEDbeNkjmDoE+ePNnt/9zHjx8RQhYWFlh+P3HixOfPn8eMGTN58uTnz5/zHoSCgoKbm9ulS5eEGXm6YsUKfueJsNns4uJiwZrDODs7m5qaZmRkIIR8fX2FmZaJrQO1bdu2w4cPCxMSQujff//lpVheXp69vT0uQ31TU1Pz8/NnzJjBvRi2gIynp6ecnFyvJf/++29x+HFWXl4eHx+fmJgoKytbUVHBZrN7fZl9rbGxESFUU1MjZD3t7e2FhYW5ubk5OTn5+flNTU2NjY1YH6mqqqqcnJyysvLw4cP19fV1dHQ2bdpkaWm5cOFCYVpksVh//fVXYmKikJHjgkajFRUVmZiYiMlo96KiIhkZGe4znLv66aefekziTCYTu1IzMzOzs7PrWqCsrKy0tBR16Et58uQJ9nZs2bKFrySOEKLT6RQKRZh3s9e80C0pKSmBW0QI3bx5k5NohFz6Q0w+SYIhkUhkMp5zDnCvUEhSUlJiFQ9CSLB4mEzmq1evnj59+vTp05cvX2K3vslk8uDBg9XU1BQVFbERTVVVVc3NzbW1taWlpZxFg2VkZDZu3Dht2jR7e3t5eXkcXwshSCSStLS0+PzdCfAZI5FIsrKyPQ4x5OzY0NNwoqtXr2IFoqOjOz21efNmhNDhw4d5HCJTV1eH3fLmdUwNToQZYshms58/f06lUju+p69fvxa4NhyHGI4dO5aXT8CoUaOEbwtjbW3t5ubWazFehhhihg4dum7dOjxCE9Z3M8TwzZs3a9aswS70ZGVlp02btm3btri4uMzMzNbW1p7OYjAY6enpKioq48aNmz17tqqqKkJIUVHR09MzPj6+ra2NrxhgiGFf6DHxFxUVYQeDBw/utgAny3cdmsKv6OjolpaWZcuWCVmPKH38+HHOnDktLS1GRkZ//PEH9iBnWRVizZ07l5di8+bNw6vFwYMHC9kx1VFbW1tVVRW/vytBt9rb28+ePTt27FhLS8uzZ886OTk9ePCgrq7u2bNnu3btmjdv3ujRo7l0c0tJSV28eLGlpeXq1au3bt369u1bamrqL7/88uLFCxcXlxEjRuzZs0f4jh0gjB6T+Ldv37AD7JZdV1gS19LSwtYXFUZkZKSNjQ12m1QilJaWOjo61tbWDhgw4M6dOwEBAUOHDkUIJSYm8tuP1Bd+/fVXFRUV7mWUlJTWrl2LV4tTpkxJTU3lcY31Xj169Ki9vX3atGm41NZv0en0w4cP6+vrL1u2TF1d/dq1a5WVladPn7a3t+e977HT3j1kMtnCwiIsLKygoODFixfTp08PDg4eMWLE2rVrORkDiFiPSVxLSws7wO7adVJaWvr27Vsk3DQfTFZW1tu3b318fISsR2Tq6uqcnJxKSkqoVGp8fLyuri6FQuEkRGzVFGJpamqeP3+eS/8amUw+e/bsgAED8Gpx3rx5TCbz9u3buNR28+ZNbW1t4T9a/dn9+/fHjRu3bt26CRMmYJ3g8+fPF2BgSU+ze0gk0uTJky9duvT582dfX98///xz5MiRx48fZzAYOL0CwKse/845Ew7v3LmTnp7e8anm5mZvb2/sdofwf2mRkZFKSkpC3vUWmdbWVhcXl8zMTDKZfPHiRU5X0sqVK7FR0klJSU+ePCE0RoQQmjNnTnx8vLq6eten1NTUbty4gWNfCkJIR0dnwoQJx44dY3OdYcSLr1+/RkdHL1y4UHzuOEmWysrK+fPnOzo6Kioqvnz5Mi4uzsrKSrCqeJndM2LEiEOHDv3777/29vYBAQHjx4//559/BI0dCKLHJG5qajpu3DiEEJvNdnJyunPnTltbW01NzfXr1y0tLR8+fIgVEzKJt7e3nz9/3t3dXSJudrNYLE9PT2wI/MGDBzvmQUVFRc4kCHG4GEcIzZo1Ky8vb8+ePVZWVtgXjImJya5du/Ly8ubMmYN7czt37kxLSxN++YSdO3e2t7f3nz008PXgwQMzM7OkpKRTp069fftW4PSN4X12z/Dhw69cufLkyZP29nZra+s//vhD+K9zwCsuC2DFxcV1/EnOGQJoZWWFze5BCFVXV3c9kffRKXFxcQihV69eCXV3VlD8jk7x8/PDXnVAQEDXZ798+cIZrHLv3j1+g8F9AayOsA2GkpOT+6JyjunTpw8ZMqS8vLynAr2OTnn27BmFQhH9OCUuJGV0CoPB2LJlC5lMnjx5cmFhofCtYPvfxsTE8HUWjUbDVvF0cHDomhxgdEpf4DYscd68eVFRUZxrZAaDYW5uHhkZ+eLFC+wWloGBgZCrKERGRhoZGQl5vSAaISEhJ06cQAi5uLh0Ox9HS0vL29sbOxaTi3ERi4yMpNPp2KAdAU4vLi5euHDh2LFjt27dints37fW1taFCxeGhYVt2rTp6dOnI0aMELLC9vb2zZs3CzC7R0FB4a+//oqNjX39+vXUqVNhnyYR6GVsuZeXV3l5eVJSUmpqamNjY1pamre3d1lZGTb1Tsi+lIqKirt37y5fvlyYSkTj9OnTWF6eMGHC5cuXe7pnuGHDBmz2UEpKCo9z378nOjo6MTEx79+/d3Fx6WlQU08+fvz4448/SktLx8fHS0Tfmvioq6tzcHC4c+fOhQsX9uzZ02l5DMFERETk5uYKPIN64cKFL168aGpqsra2hi7yvtb7BCEVFRUbGxsLCwvO4tTYuBQkdBLH9i1bunSpMJWIQEJCws8//4wQ0tHRSUhI4JJidHV1Fy1ahB0HBQWx+1+3oK2t7bVr1968eWNpacn7X29sbKy1tTVC6OHDh0OGDOnLAL83bDbb1tb2n3/+SUhI8PDwwKVOXPbuGT169PPnz9XV1e3s7AT7ZQZ4JMjM3ZSUFOxAyCQeGRk5a9asgQMHClNJX3v9+vXixYuZTKaqquqdO3d6jXbTpk3YQXp6Otbj39/MmTPn5cuXbDZ74sSJS5cu/fz5M5fCz58/nzZt2qJFiywtLd+8eWNsbCyyOL8PJBLJ0dExKSkJxxVddu/ejcvePcOHD09OTj5x4kSnic0AX4L88sKuxKWlpc3NzTs+fufOnQ8fPiCEsEVEHz582NraihCysrKysbHpVMmLFy9ycnL2798vWNyikZ2dPXv27ObmZgqFEhcXx0uKMTU1dXR0vHfvHkIoODh43rx54rbmhgiMGTPmw4cPx48f37t374ULF8zMzFxcXExMTLAtRF6+fEmn01NSUuLj44uKigwNDWNjYxcsWABjCgUTGhqKY23Y7J7Vq1fjsquJuro6Xr8PQE/4TuJsNjstLQ0hNG7cuE7zvmJjY8+cOcP5Z0JCQkJCAkJo8+bNXZN4ZGTkwIEDnZ2dBQhaZIyMjASYhXj37t2+CEayyMnJbdiwwdfX9/r16zdu3Ni/fz/nN7W7uztCSFNTc86cOa6urs7OzhQKhdBgwf/v9OnT8vLysHePBOE7iWdnZzc0NKDulkyJioricU1wGo0WExPj5+eHy00YILZUVVW9vb29vb0ZDEZVVVVxcfE///wzbdq0QYMG4ThfFODot99+8/Ly6naaGBBPfOdQXDrEY2NjaTQaZ0Ae+O5JS0sPGTJkyJAh2A1MILY0NDRg9zXJwncS9/DwWLBgARJ0/W5MVFSUtbU13MUCAAAhSevq6vK4ozGGQqEI34NZXl4eEhIiZCUAAACkjx49KvpWuQ87AwAAwKN+N/oNAAC+J5DEAQBAgkESBwAACdavkzibzd6wYQNJPBgZGSGESkpKiH5XAACSpF/PtVm3bh2VSlVSUiI6EIQQYrPZHz58kJQdjgCBsBUi586di+9cudbWVhaLha3vRqfT29racP/TYDKZ2Lr5vFNUVCSRSBI3p7e5uXnKlCmPHj0SQVv9OolzdqkHQIJYWlq6urrq6+vjm9pu3rzZ0NCArSqanJz8zz//rFy5Esf6EUL//vsvv3W2tLT88MMPXeeHi7nz589jq1KLQL9O4gBIInl5+Rs3buBebUFBQXFxMbac1u+//56dnY3v0lqCIZFIzs7O//3vf4kOhD9JSUkiW7qgX/eJAwCApIMkDgAAEgySOAAASDAyg8Gg0+kibrWtrU3ELQIAgJDYbDa/m8eKANnPz++nn34Scas6OjoREREibhQAAIRx9OjRoUOHMplMogP5H+TKysrKykoRtzp+/Phjx46JuFEAABBYbW3trl27XF1dRTZ2kEfE9Il7e3tnZ2e/fv2akNYBAIBfO3fubGxs3LVrF9GBdEbMOHEXFxcNDY3IyEgrKytCAugnSktL7969m5OTk5GRgRAKCgqysLAwNDR0cnIaNmwY0dEBIDHy8/NPnDjx22+/6evrEx1LZ8QkcRkZmSVLlpw5c+bw4cPYNF+AIyaTee7cuYiIiLS0NBKJNHDgQEVFRYRQSUlJdnZ2VVUVm822sLBYtWrVsmXLxO23IQBiaNOmTfLy8ps2bSI6kG4QNsTQx8enoaHh2rVrRAXwvXrw4IGpqamPj4+KisrJkyfLysrKy8svXLiAEIqKiiovLy8vLz916pSqqqqvr++4ceMSExOJDhkAsfb69etr167t2LFDPPePJiyJm5qampubR0VFERXAdyk0NNTR0VFeXv7JkycPHz5cuXLloEGDOpUZOHDgihUrHjx4kJSUpKio6OTktHv3bjabTUjAAIg5bK1TPT29n3/+mehYukfkZB8fH5+kpKSCggICY/husNlsX1/fLVu2rF69+uXLl7a2tr2eYmNj8/Lly19//XXbtm3e3t6QxwHoKiYm5sWLF/v375eRkSE6lu4RmcQ9PT1lZGTOnDlDYAzfjT179pw+ffro0aNHjhzhfYVSKSmpQ4cOhYeHnz17VgxvuwNALDqdvm3bNmtr67lz5xIdS4+ITOLq6uqurq5nzpxhsVgEhvEduH37dlBQ0Nq1awMCAgQ4/ZdfftmwYcP27dsTEhJwjw0AyXXs2LG8vLwDBw6QSCSiY+kRwWuneHt7FxcXP378mNgwJFp7e/vatWutrKz2798vcCWhoaFTpkxZu3at6NdgAEA81dbW7tmzx8PDY/LkyUTHwg2vSZzNZicmJnp5eU2aNMne3n7r1q0VFRUIoQ0bNhgbG48ePVqw5VBmzpw5dOhQuL0pjD///DM3N3f//v3CDBaUkpI6ePBgXl7en3/+iWNsAEiunTt30mi0nTt3Eh1IL3hK4mVlZXZ2dg4ODufPn09JSXn06NHevXuNjY2TkpISEhKys7OlpKRkZWUFaZ5M9vLyiouLq6urE+B0gBA6fvz4nDlzhL9YmDhxoqur69GjR3GJCgCJJs6zezrpPYnn5eVNnDgxKSkJISQvL+/p6RkSEuLr60uj0ebNm5eTk4MQmjRpksAReHt7t7a2RkdHC1xDf5abm5udne3h4YFLbe7u7rm5uR8/fsSlNgAklzjP7umkl2EM9fX19vb2WM/JtGnTYmJiOOOO7ezsPD09seNOO+DRaDQqlcrjr3sDA4Np06ZFRkauWrWK7/D7vZs3b1IoFCcnJ1xqc3JykpWVvXXrlomJCS4VAiCJsNk9R44cEc/ZPZ30ciW+Zs2awsJChNDy5csfP37cceaIu7u7np4edoxdiTOZzEOHDunp6SkrKyspKU2ePPnixYu8BOHj45OSkpKZmSnYa+jPPn36ZGhoqKqqikttysrKI0eOxH5dAdA/if/snk64XYm/f//+7NmzCCFDQ8Pw8PBOo49JJJKBgUF+fj6VSh09ejRCaNmyZRcvXlywYIGXl1d2dnZ8fPx//vOfJ0+e/P3339yDcHNzCwgIiIqKEmb7+ZqaGqI61uvr61VUVAhpOjc3V1VVNT8/n3uxsrIyhFB5eXmvJVVVVXNycnotJjAC3yvBtLe3NzQ0ZGZmSktLNzc3M5nMvntziNXU1NTW1pabm9va2lpbW8tiscTklfbFNLS6ujrs9SorK8vKyiopKXGewmb3xMXFCTO7h8Vi0Wg0vt7A5uZmaWlpfhsdMmQImj17tq2tLbs7S5cuxco9evSo2wJDhw5FCE2dOpXNZl+9ehUhdPnyZc6zWVlZWIGrV692e3pH3t7egwYNYrFYvZbsycCBA/l68QAAibB48WKB0wKbzf769WtcXNy2bdsWL148fvz4nq4hhgwZYmNjs2zZMg0NjTFjxrS2tgrTqJqammjenICAgB6vxJlMZnx8PELIzMzMzs6ua4GysrLS0lL0f30px44dc3R0dHd35xQwMTH5448/Fi9eHBISsmDBAu6h0Ol0CoUizIj6hIQEombw5+fnDx8+nPd5kjjavn07mUwOCgriXuzz589bt27duXOnkZER95IhISF0Or2PhlUxmczCwkLxv93fUUBAgJmZ2Zw5c2RkZE6cOMFkMrdt20Z0UH3i0KFD1dXVmzdvptFoz549u3//fmRkJNFBIXd393HjxvF7FpvNfv78+dWrVx8/fpyVlcVms5WUlAwNDQ0NDWfNmqWmpqaoqIh1Qra3t9NoNBqNVlJS8vnz5zt37nz79u3bt29qamqTJk2aNWvWokWLRowYwW8AI0aMMDY2/u2333g/5cuXLzIyMnx1jZJIpKlTp/Z4Jc7ZsWHt2rXdftVgl94IoejoaDab7e3tfenSpU5lmpqayGQyhUKh0+lcvrXq6uqoVGpgYKBgX3r9mbe399ixY3st9ubNG4RQcnJyryVNTU29vLzwCO07oa+v7+/vjx07OTnNmDGD2Hj6zqJFi6ysrLDjbdu2qaurExsPRkpKat++fbyXz8nJ2bRp0/DhwxFCmpqaixcvDg8Pz8zM5OVXfk1Njbq6+qJFix4/frx9+3Y7OztpaWkSiTR58uSIiAgajcZ7GJaWlkL+gOBdjxePRUVF2MHgwYO7LcDJ8tjQlPDwcAaD0akMlUpVUFBobGysra0dMGBAT21FR0e3tLQsW7as968e8L90dXWvXLnS0tJCpVKFr621tTUvL0+cl4kAoCcpKSn79u2Li4uTl5d3dXX19PScMWMGhULhvQZsds+ePXv09fWnT5+OEPr69evVq1ejo6P9/f1///13Pz+/1atXi1vPbY+jU759+4Yd9LS7M5bEtbS0dHR0EEJUKrXjzQHMp0+fGhsb1dXVuWRwhFBkZKSNjY2BgQE/kQOEEHJ2dm5ubn748CEutT169IhGo82aNQuX2gAQjY8fPzo4OEyaNOnVq1dhYWFlZWUXLlxwdnbmK4N3O7tHS0vLz8/v6dOnmZmZrq6u+/fv19HRCQwMbGpq6oPXIaAek7iWlhZ2gO3s1Ulpaenbt29Rb9N87ty5gxDy9fXlUiYrK+vt27c+Pj68hAs6GT9+/LBhw2JjY3Gp7erVq0OGDJkwYQIutQHQ1xoaGtavX29mZpaVlXX69On8/PwNGzYoKysLUNXGjRsVFBR6mt1jYmJy+vTpgoKClStX7tu3b9SoUVjvsXDh46PHJG5oaIgd3LlzJz09veNTzc3N3t7e2EpJXJJ4WVlZSEiIvr7+li1buEQQGRmppKS0cOFCvuIGGBKJ5Ovre/ny5U+fPglZVU5OzsWLF5cvXy7OC7YBwPHkyRMTE5Pjx4+vW7cuOzvbx8dH4EGBr1+/jouL2759O/fZPdra2keOHElPTzc2Nl6yZMmsWbO+fPkiWIs46jGJm5qaYjeF2Wy2k5PTnTt32traampqrl+/bmlpyfn93lMSb2homDVrFoVCuX37Npf7re3t7efPn3d3d4edNgW2bt06TU1N4ecHb9myRU1NbcOGDbhEBUDfYTAYv//+u729/dChQz98+BAaGortIisYNp+ze0aPHv3gwYNLly69fPnS1NSU8A0Ouc3YxIavIYQqKytnzZqlpKSkqak5f/58RUVFbHYPQmjixIldT2xoaHB0dKyrq3v+/PmoUaO4NJGQkPD161foSxGGoqJiSEjIzZs3hVm7Kjw8PC4uLiQkpOuNDQDEyrdv33788cfdu3evX78+OTl55MiRQlYo2N49Hh4e6enpenp6jo6OxG6owi2Jz5s3LyoqinONzGAwzM3NIyMjX7x4UV1djRAyMDDQ0NDodFZDQ4ODg8PXr1+fPXvG6ZPpSWRkpJGRkZWVlRAvAaDly5cvX758/fr1t2/fFuD0+/fvr1271tvbe8WKFbjHBgCOiouLp02blpGRcfv27X379vF167Jbwuzdo6Oj8/Tp07Vr1wYFBa1cubLr8DzR6GV+ipeXl6ura3p6uqKiopGRkYKCAkKopKSkqqoKddeXUl9f7+DgQKPRkpOTu27R20lFRcXdu3dDQ0OFiB/8PxEREfn5+XPnzj1y5Mgvv/zC+4knT5789ddfJ0+efOLEib4LDwDhZWVlOTo6MpnMp0+fmpqa4lLn0aNH8/Lyzp07J9itIGlp6T/++GPYsGHr16+vrKyMjY0VbFFuYfS+FK2KioqNjY2FhQWWwRFC2LgU1CWJ19fXz5w5k06nJyUl9ZrBEULYG8eZ3A+EISMjc/fu3f/85z/+/v7u7u68TF4tKiry8PDw8/Pz8PC4f/++6D98APDFz8+PSqU+f/4crwxeW1u7d+9eDw8Pa2trYer57bffLl++jM0OxSUwvgiyPVtKSgp20DGJ19XVzZgxg0QiPX78WFNTk5d6IiMjZ82aJW4j5yWXrKxsVFRURETEgwcPjI2N/f39nz59ymQyOxVjMpnPnj1bvXr1qFGjEhMTjx8/fvbsWcjgQPxdvHgxJSWFs3iq8HDcu2fRokUNDQ3jx48Xvip+CbLcB3YlLi0tbW5uznkQW07WxsZm6dKlbDa7U+6IjIzU1tbu+MiLFy9ycnKE2RYSdAu7sg4NDf3rr78iIiKw1XywHL1jx4729vasrKzq6mo1NbVff/0VG5FCdMgA8GTYsGE41pafnx8REbFmzRq8FvPBhoGIHt9JnM1mp6WlIYTGjRsnJyfHefzr168IoadPn3Z7VnNzc6dHIiMjBw4c6OzszG8AoFeqqqqhoaEhISHPnj27fft2bm5uQUGBlJRURUWFnp6el5eXs7OzjY0NISt2ASAmKioqTE1Nt27dSnQgwuL7zzg7O7uhoQF12c0nOTmZ90poNFpMTIyfnx/kkb4jLS1tZ2fX7QqUAIApU6Zwbu9JNL6v/7vtEOdXbGwsjUbz9vYWuAYAAABIgCtxDw8PbHHwjn0p/IqKirK2tjY2Nha4BgAAAAghaV1dXRqNxvsJFApF+AH25eXlISEhQlYCAABAWpi52gL7/Pmz6BsFAIDvDzFjYgAAAOACkjgAAEgwSOIAACDBYJg2AEB8sdns9+/f47V3FaalpaW0tBRbY5XJZGZnZ3PW1sZLTU0N9z0pcQRJHAAg1i5cuHDhwgWio+AbLnuX8wKSOABAfJWXl+O+K/Gff/554MCBnJwchNCDBw9WrVqVlJSE78IsDAZj+PDhOFbIBSRxAID46otVTtXV1UkkErYaIlb/sGHDcFwcUcTgxiYAAEgwSOIAACDBIIkDAIAEgyQOAAASDJI4AABIMEjiAAAgwSCJAwCABIMkDgAAEgySOAAASDBI4gAAIMH6MIkXFRXt2LHD2tpaW1tbVVV17Nixrq6ud+/e7bsWAQCgv+mTtVPa2tpCQkJCQ0MZDAbnwfr6+szMzPj4eFtb2ydPnvRFuwAA0N/gn8QbGxudnZ2fP3+OEJo4caKbm5uOjk5NTU1hYWF0dHRhYaGOjg7ujQIAQP+EcxJnMBhYBpeTkzt58uRPP/3U8dkdO3aEh4dPmTIF30YBAKDfwjmJBwUFYdfgFy5cWLBgQadnZWRk1q5d2/EROp3e3NysqqqKbxgAANBP4Hljs6CgYP/+/QihOXPmdM3gnWRkZMycOZNKpaqpqenq6p46dQrHSAAAoJ/A80o8LCwMu5MZGBjIvWRaWtr06dPJZPK6devU1NTi4uJWrVpVVla2c+dOHOMBAIDvHm5JnMViXbt2DSFkbm5uaWnJpSSbzV6+fDmDwXj16pWpqSlCaNOmTU5OTnv27Fm8eDHuO5YCAMB3DLck/uHDh+rqaoTQmDFjuJdMT0/PyMgICAjAMjhCSEpKKiwsbPz48WFhYefOnRMsgN27dxcXFwt2rpBSU1ONjIwUFRUJaZ0XDAbjn3/+MTMzk5GRITCM5ubmrKysCRMmkEgkAsPgy9evX5OSkn788Uc5ObnMzEw2m/3zzz8THVSfSE1NpdForq6udXV1NBqtqanpe32lGRkZLBbL09MzJydHQ0MDIRQYGKisrExsVJ8/f5aTkxs6dChfZ82fPx+3JF5SUoIdjBo1invJe/fuIYQcHBw6Pmhubq6lpZWcnCxwAKmpqZwYRInNZn/+/LmlpUVeXl70rfOIwWDk5+ezWCwKhUJgGK2trdj/EZksMVOF29ravnz5UlNTQ6FQGhoa2Gx2Wloa0UH1idraWjqd/uHDh6amJikpKSaT+b2+0srKSjabnZ6eXl5eXltbixDKzMyUlZUlNqry8nIKhVJVVcXXWaampoiNk9u3b2OVBgUFcS9pZ2eHECoqKur0+NSpUxFCFRUVeIUEgPD09fX9/f2xYycnpxkzZhAbT99ZtGiRlZUVdrxt2zZ1dXVi4+k7YWFh0tLS2PH169cRQnl5ecSGJAzcLoiMjY2xg6ysLO4lKyoqEEJDhgzp9Liuri5CKDc3F6+QABCelZUVp9/PwsLCwsKC2HgA6AS37pQRI0YMHjy4vLz85s2bHz9+NDEx6VTg/fv3ycnJ/v7+9fX1ZDJZSkqqUwEqlYoQampqEiyA6OjooqIiwc4V0rt374yMjLD4xROTyXz37p25uXnXt12U2traMjMzx48fL0F94mPHjq2pqfn555+pVKq2tjZCKCwsjOig+kR2dnZdXd2GDRtqa2sLCwtbW1u/11f69OlTFosVHByck5ODdTCeOnVKXV2d2KgKCgpkZWUHDx7M11kODg64daew2ewzZ85g9Wpra8fExHz9+rW5uTk3N/fixYtz584lk8mrV69ms9mKiooyMjJdT//ll18QQrGxsYK1bmRkhPvbyiOJSEliEqSYhAEA+i4+jUFBQXgmcRaL5ejo2FNjKioq165dY7PZmpqaZDK56+krVqxACCUkJOAYEgCAR9AnLqHwHCRAIpFu3rwZHByspqbW8XEjI6P9+/cXFxfPnz8fIaSqqspisdrb2zud3tbWhj2LY0gAAPB9w3ntFBkZme3btwcGBmLDxlVUVHR0dAYOHNixDJamS0pK9PT0Oj5eWlqKEFJRUcE3JAAA+I71yXriFApl/PjxPT07cuTI1NTU3NzcTkk8MzNTTk4OG6MCAACAFwTMuXB1dUUIvX79uuODubm5X758sbOzU1BQEH1IAAAgoQhI4k5OTrKyslFRUS0tLZwHjx49ihBycXERfTwAACC5CEjiSkpKGzduLCoqWrRoUX5+fktLy8GDB8PDw0eNGtVpEwkAAADc9UmfeK+Cg4NramoiIiISEhKwR8aOHXvz5k05OTlC4gEAAAlFTBKXkpI6fvy4v79/YmIijUYzMzNzcnKSoEWRAABATBCTxDHGxsacFVcAAAAIAC5+AQBAgkESBwAACQZJHAAAJBgkcQAAkGCQxAEAQIJBEgcAAAkGSRwAACQYJHEAAJBgkMQBAECCQRIHAAAJBkkcAAAkGCRxAACQYJDEAQBAgkESBwAACQZJHAAAJBgkcQAAkGCQxAEAQIJBEgcAAAkGSRwAACQYJHEAAJBgkMQBAECCQRIHAAAJBkkcAAAkGCRxAACQYH2YxIuKinbs2GFtba2tra2qqjp27FhXV9e7d+/2XYsAANDfSPdFpW1tbSEhIaGhoQwGg/NgfX19ZmZmfHy8ra3tkydP+qJdAADob/BP4o2Njc7Ozs+fP0cITZw40c3NTUdHp6amprCwMDo6urCwUEdHB/dGAQCgf8I5iTMYDCyDy8nJnTx58qeffur47I4dO8LDw6dMmdLxQSaT2dLSoqioiG8kAADQH+DcJx4UFIRdg1+4cKFTBkcIycjIrF27dtKkSZxHCgsLp0+ffvr0aXzDAACAfgLPK/GCgoL9+/cjhObMmbNgwQIuJa9cufL8+fOsrKynT5+yWCzuhQEAAPQEzyvxsLAw7E5mYGAg95InTpy4fv26jIzM5MmTcQwAAAD6G9ySOIvFunbtGkLI3Nzc0tKSe+EnT56Ulpbeu3dv6tSpeAUAAAD9EG7dKR8+fKiurkYIjRkzptfCJBIJr3Y59PX18/Pzca8WgH6l499mX/ydio+Or05fX5/ASISxefNm3JJ4SUkJdjBq1Ci86uTLkSNHysvLCWn63bt3RkZGVCqVkNZ5wWKx0tLSxo8fLyUlRWAYbW1tmZmZFhYWBMYgmIKCAjk5OW1tbaID6UN//fVXTU2Nj49PXV3dx48fnz59evDgQaKD6hP379+/cePGH3/8kZOTgxA6ceLE7t27NTU1iY1KsM/Y1KlTcUviZPL/65mh0+l41cmX2bNnE9IuAN+Hx48fUygU7IZWUFDQ27dvV65cSXRQfaKuri4+Pv63335DCN24cePEiRPu7u56enpExyUg3JK4sbExdpCVlYVXnQAAkVm3bl1DQwN27OXlxUu/KBAHuCXxESNGDB48uLy8/ObNmx8/fjQxMelU4P3798nJyf7+/ni12MmMGTMI6RNns9kVFRUaGhqysrKib51HTCazqqpqwIAB0tJ9stACj+h0enV1tba2tsR1tn779k1aWlpFRYXoQPpcY2Nja2urlpYWQmjLli1Eh9Mn6urqmEzm0KFDa2pqlJWVEUK2trYUCoXYqAT7jAUEBODZnbJnz55ly5YxGAx7e/sjR45Mnz5dQUGhrKzs7du3sbGx8fHxv/zyC17NdeXg4JCbm9t39XORnp4+cuRIeXl5QlrnBYPBeP/+/dixY4n9pLa0tGRnZ5uZmUlcEs/Pz5eTkxs8eDDRgfS5L1++NDQ0GBgYEB1IH8rIyEhJSbG1tf38+bOKikpiYuKUKVOwbE6ggoICWVlZfj9jpqamiI0fFovl6OjYU2MqKirXrl3rdMrmzZsRQocPH8YxDAAA4CIsLExaWho7vn79OkIoLy+P2JCEgedkHxKJdPPmzeDgYDU1tY6PGxkZ7d+/v7i4eP78+Tg2BwAAAOceUhkZme3btwcGBmLDxlVUVHR0dAYOHIhvKwAAADB9cpuLQqGMHz++L2oGAADQEWzPBgAAEoyYAWd37tz58OEDQujVq1cIoYcPH7a2tiKErKysbGxsCAkJAAAkETFJPDY29syZM5x/JiQkJCQkIIQ2b94MSRwAAHhHTBKPioqKiooipGkAAPieQJ84AABIMEjiAAAgwSCJAwCABIMkDgAAEgySOAAASDBI4gAAIMEgiQMAgASDJA4AABIMkjgAAEgwSOIAACDBIIkDAIAEgyQOAAASDJI4AABIMEjiAAAgwSCJAwCABIMkDgAAEgySOAAASDBI4gAAIMEgiQMAgASDJA4AABIMkjgAAEgwSOIAACDBIIkDAIAEgyQOAAASDJI4AABIsD5M4kVFRTt27LC2ttbW1lZVVR07dqyrq+vdu3f7rkUAAOhvpPui0ra2tpCQkNDQUAaDwXmwvr4+MzMzPj7e1tb2yZMnfdEuAAD0N/gn8cbGRmdn5+fPnyOEJk6c6ObmpqOjU1NTU1hYGB0dXVhYqKOjg3ujAADQP+GcxBkMBpbB5eTkTp48+dNPP3V8dseOHeHh4VOmTMG3UQAA6LdwTuJBQUHYNfiFCxcWLFjQ6VkZGZm1a9d2fIRGo1GpVCkpKXzDAACAfgLPG5sFBQX79+9HCM2ZM6drBu+IyWQeOnRIT09PWVlZSUlp8uTJFy9exDESAADoJ/BM4mFhYdidzMDAQO4lly1btn79egsLi6CgIBcXl/T09P/85z++vr44BgMAAP0Bbt0pLBbr2rVrCCFzc3NLS0suJa9du3bhwoXLly+7u7tjj3z8+NHBweH06dNOTk7cL+EBAAB0hFsS//DhQ3V1NUJozJgx3EseO3bM0dGRk8ERQiYmJn/88cfixYtDQkIETuJ37twpLS0V7FwhZWRkjBo1Sk5OjpDWecFisd69e2dubk4mEzm9i06nZ2VlmZubExiDYAoLC6lU6sCBA4kOpM9VV1fX1dUZGBgQHUgfevPmDYvFOnLkSG5uLovFQghFR0dramoSG1VhYaGcnNygQYP4OuuHH35AbJzcunULqzQkJIR7SW9v70uXLnV6sKmpiUwmUygUOp0uWAAwchEA0N9s3LgRtytxziUenU7nXjI8PLzjJCAMlUpVUFBobGysra0dMGCAAAEUFBQIcBYAoL/Zt29fYGBge3s7QujGjRvz5s3Ly8vT09MjOi4B4ZbEjY2NsYOsrCzuJalUatcHP3361NjYqK6uLlgGBwAAHmloaGhoaHCOZWRklJSUiA1JGCQ2m41LRSwWa9iwYeXl5dLS0hkZGSYmJp0KvH//Pjk52d/fv9vTDx48uH79+o0bN4aFhQkWQFZWVkVFhWDnCqmwsHDYsGFiPto9Ly9PX1+f2BjYbHZhYaGuri6xYQjg69evsrKyysrKRAfS55qamhobG/ntmZU4bW1tUlJSZWVlI0aMaGtrk5WVJToi9PXrVxkZGRUVFb7OMjMzw61PnM1mnzlzBqtXW1s7Jibm69evzc3Nubm5Fy9enDt3LplMXr16dbcnlpaWqqmp6evr19bWCtw6XMIDAPqb1atX43YljhBis9nOzs737t3r9lkVFZXIyMj58+d3eryhoeGHH36oqKh49uzZqFGjBG69rKyssrJS4NOFUV1draGhQSKRCGmdR9XV1YTffxefMPjV2NhIoVDEeQASXuh0ektLC7/Xg5KIzWbX1NRw+lUIJ9hnzNjYGM8kjhCi0+l79uw5evRobW0t50EjI6Ply5evXLmy66/RhoYGR0fH8vLyBw8eGBoa4hgJAAD0BzgncUx7ezs2bFxFRUVHR6en0bUNDQ0ODg7V1dWPHj0aPnw47mEAAMB3r0+SOC/q6+sdHBxoNNrDhw+/+7soAADQR/pkU4he1dfXz5w5s729PSkpSRJ7SAEAQEwQkMTr6upmzpxJJpMfP36sqqoq+gAAAOC7QUB3yvz5869fv25jY6OkpMRms5lMZsdnIyMjtbW1RRwSAABIKAKuxL9+/YoQevr0abfPNjc3izYcAACQYP8fSb5rjU8aVpcAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, - "execution_count": 84, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -222,20 +232,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Compile and Run or Execute " - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [], - "source": [ - "# Create a Quantum Program for execution \n", - "qp = qiskit.QuantumProgram()\n", - "# Add the circuit you created to it, and call it the \"bell\" circuit.\n", - "# (You can add multiple circuits to the same program, for batch execution)\n", - "qp.add_circuit(\"Circuit\", circuit)" + "### Execute " ] }, { @@ -247,7 +244,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -256,12 +253,16 @@ "text": [ "(Local Backends)\n", "local_qasm_simulator\n", + "local_clifford_simulator\n", + "local_qiskit_simulator\n", + "local_sympy_qasm_simulator\n", + "local_sympy_unitary_simulator\n", "local_unitary_simulator\n" ] } ], "source": [ - "local_backends = qiskit.backends.discover_local_backends()\n", + "local_backends = discover_local_backends()\n", "print(\"(Local Backends)\")\n", "for backend in local_backends:\n", " print(backend)" @@ -269,7 +270,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -281,28 +282,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next we need to compile the circuits into a quantum object which we call qobj" + "Next we need to run the circuit" ] }, { "cell_type": "code", - "execution_count": 64, - "metadata": {}, - "outputs": [], - "source": [ - "qobj=qp.compile(circuits, backend) # Compile your program" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Then you can run your program. Using wait and timeout we can check the execution result every 2 seconds and timeout if the job is not run in 240 seconds. " - ] - }, - { - "cell_type": "code", - "execution_count": 65, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -314,7 +299,12 @@ } ], "source": [ - "result = qp.run(qobj, wait=2, timeout=240)\n", + "# Create a Quantum Program for execution \n", + "qp = QuantumProgram()\n", + "# Add the circuit you created to it, and call it the \"bell\" circuit.\n", + "# (You can add multiple circuits to the same program, for batch execution)\n", + "qp.add_circuit(\"Circuit\", circuit)\n", + "result = qp.execute(circuits, backend, wait=2, timeout=240)\n", "print(result)" ] }, @@ -322,7 +312,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "When you run a program, the result will be a new object that contains the data, status, and a copy of the qobj. The status of the results can be obtained using print and will one of the follow:\n", + "When you run a program, the result will be a new object that contains the data. The status of the results can be obtained using print and will one of the follow:\n", "\n", "```\n", "JOB_STATUS = {\n", @@ -331,7 +321,15 @@ " errorExecuting: 'ERROR_RUNNING_JOB',\n", " completed: 'COMPLETED'\n", " };\n", - "``` " + "``` \n", + "\n", + "#### Execute Parameters \n", + "Execute has the combined parameters of compile and run.\n", + "\n", + "```qp.execute(name_of_circuits=None, backend='local_qasm_simulator', config=None, wait=5, timeout=60, basis_gates=None, coupling_map=None, initial_layout=None, shots=1024, max_credits=3, seed=None, hpc=None)\n", + "```\n", + "\n", + "(**Tip**: You can obtain the above parameters in Jupyter. Simply place the text cursor on a function and press Shift+Tab)" ] }, { @@ -346,7 +344,7 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -355,7 +353,7 @@ "{'101': 1024}" ] }, - "execution_count": 66, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -364,123 +362,6 @@ "result.get_counts('Circuit')" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In addition to getting the number of times each output was seen, you can get the circuit which was run in QASM format.\n", - "For this simulation, the compiled circuit is not much different from the input circuit. Each single-qubit gate has been expressed as a u1, u2, or u3 gate." - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "OPENQASM 2.0;\n", - "include \"qelib1.inc\";\n", - "qreg q[3];\n", - "creg c[3];\n", - "u3(3.14159265358979,0,3.14159265358979) q[0];\n", - "u3(3.14159265358979,0,3.14159265358979) q[1];\n", - "barrier q[0],q[1],q[2];\n", - "u2(0,3.14159265358979) q[2];\n", - "cx q[1],q[2];\n", - "u1(-0.785398163397448) q[2];\n", - "cx q[0],q[2];\n", - "u1(0.785398163397448) q[2];\n", - "cx q[1],q[2];\n", - "u1(-0.785398163397448) q[2];\n", - "cx q[0],q[2];\n", - "u1(0.785398163397448) q[1];\n", - "u1(0.785398163397448) q[2];\n", - "u2(0,3.14159265358979) q[2];\n", - "cx q[0],q[1];\n", - "u1(0.785398163397448) q[0];\n", - "u1(-0.785398163397448) q[1];\n", - "cx q[0],q[1];\n", - "cx q[0],q[1];\n", - "measure q[0] -> c[0];\n", - "measure q[1] -> c[1];\n", - "measure q[2] -> c[2];\n", - "\n" - ] - } - ], - "source": [ - "ran_qasm = result.get_ran_qasm('Circuit')\n", - "\n", - "print(ran_qasm)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can use \n", - "\n", - "```qp.execute(circuits)```\n", - "\n", - "to combine the compile and run in a single step." - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "COMPLETED\n" - ] - } - ], - "source": [ - "out = qp.execute(circuits, backend, wait=2, timeout=240)\n", - "print(out)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Compile Parameters\n", - "```qp.compile(name_of_circuits, backend='local_qasm_simulator', config=None, basis_gates=None, coupling_map=None, initial_layout=None, shots=1024, max_credits=10, seed=None, qobj_id=None, hpc=None)```\n", - "\n", - " - name_of_circuits (list[str]): circuit names to be compiled.\n", - " - backend (str): a string representing the backend to compile to\n", - " - config (dict): a dictionary of configurations parameters for the\n", - " compiler\n", - " - basis_gates (str): a comma seperated string and are the base gates,\n", - " which by default are provided by the backend\n", - " - coupling_map (dict): A directed graph of coupling:\n", - " - initial_layout (dict): A mapping of qubit to qubit:\n", - " - shots (int): the number of shots \n", - " - max_credits (int): the max credits to use 3, or 5\n", - " - seed (int): the intial seed the simulatros use\n", - " - qobj_id (str): identifier of the qobj.\n", - " - hpc (dict): This will setup some parameter for\n", - " ibmqx_hpc_qasm_simulator, using a JSON-like format like:\n", - "#### Run Parameters\n", - "```qp.run(qobj, wait=5, timeout=60)```\n", - " - qobj (dict): the dictionary of the quantum object to run.\n", - " - wait (int): Time interval to wait between requests for results\n", - " - timeout (int): Total time to wait until the execution stops \n", - "#### Execute Parameters \n", - "Execute has the combined parameters of compile and run.\n", - "\n", - "```qp.execute(name_of_circuits, backend='local_qasm_simulator', config=None, wait=5, timeout=60, basis_gates=None, coupling_map=None, initial_layout=None, shots=1024, max_credits=3, seed=None, hpc=None)\n", - "```\n", - "\n", - "(**Tip**: You can obtain the above parameters in Jupyter. Simply place the text cursor on a function and press Shift+Tab)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -490,7 +371,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -500,7 +381,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -509,26 +390,26 @@ "text": [ "\n", "(Remote Backends)\n", - "ibmqx2 {'available': False, 'busy': False, 'pending_jobs': 48, 'backend': 'ibmqx2'}\n", - "ibmqx5 {'available': True, 'busy': False, 'pending_jobs': 1, 'backend': 'ibmqx5'}\n", - "ibmqx4 {'available': True, 'busy': False, 'pending_jobs': 2, 'backend': 'ibmqx4'}\n", - "ibmqx_hpc_qasm_simulator {'backend': 'ibmqx_hpc_qasm_simulator'}\n", - "ibmqx_qasm_simulator {'available': False, 'busy': False, 'pending_jobs': 48, 'backend': 'ibmqx_qasm_simulator'}\n" + "{'available': True, 'busy': False, 'pending_jobs': 3, 'backend': 'ibmqx2'}\n", + "{'available': True, 'busy': False, 'pending_jobs': 0, 'backend': 'ibmqx5'}\n", + "{'backend': 'ibmqx_hpc_qasm_simulator'}\n", + "{'available': True, 'busy': False, 'pending_jobs': 0, 'backend': 'ibmqx4'}\n", + "{'available': True, 'busy': False, 'pending_jobs': 3, 'backend': 'ibmqx_qasm_simulator'}\n" ] } ], "source": [ - "remote_backends = qiskit.backends.discover_remote_backends(api)\n", + "remote_backends = discover_remote_backends(api)\n", "# see a list of available remote backends\n", "print(\"\\n(Remote Backends)\")\n", "for backend in remote_backends:\n", " backend_status = api.backend_status(backend)\n", - " print(backend, backend_status)" + " print(backend_status)" ] }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 13, "metadata": { "scrolled": true }, @@ -542,32 +423,6 @@ "result_real = qp.execute(circuits, backend=backend, shots=shots, max_credits=max_credits, wait=10, timeout=240)" ] }, - { - "cell_type": "code", - "execution_count": 72, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'basis_gates': 'u1,u2,u3,cx,id',\n", - " 'coupling_map': 'all-to-all',\n", - " 'description': 'A python simulator for qasm files',\n", - " 'local': True,\n", - " 'name': 'local_qasm_simulator',\n", - " 'simulator': True,\n", - " 'url': 'https://github.com/IBM/qiskit-sdk-py'}" - ] - }, - "execution_count": 72, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qiskit.backends.get_backend_configuration('local_qasm_simulator')" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -577,23 +432,23 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "{'00000': 38,\n", - " '00001': 43,\n", - " '00010': 118,\n", - " '00011': 88,\n", - " '00100': 47,\n", - " '00101': 19,\n", - " '00110': 575,\n", - " '00111': 96}" + "{'00000': 43,\n", + " '00001': 120,\n", + " '00010': 86,\n", + " '00011': 39,\n", + " '00100': 97,\n", + " '00101': 530,\n", + " '00110': 77,\n", + " '00111': 32}" ] }, - "execution_count": 73, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -602,9 +457,16 @@ "result_real.get_counts('Circuit')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see that real device gives more outcomes than the simulation as the experiment has noise. This circuit is rather complicated to implement on real hardware as it uses a CCX (Toffoli) gate and as such the effect of noise is large. Nevertheless the highest outcome is the same as the ideal prediction. " + ] + }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 15, "metadata": {}, "outputs": [ { diff --git a/reference/tools/quantum_gates_and_linear_algebra.ipynb b/reference/tools/quantum_gates_and_linear_algebra.ipynb index dd0b712eb..950df193f 100644 --- a/reference/tools/quantum_gates_and_linear_algebra.ipynb +++ b/reference/tools/quantum_gates_and_linear_algebra.ipynb @@ -4,951 +4,2419 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\"Note: Trusted Notebook\" width=\"250 px\" align=\"left\">" + "\"Note: Trusted Notebook\" width=\"250 px\" align=\"left\">" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## _*Basic Quantum Gates and Their Mathematical Definitions*_ \n", + "## _*Basic Quantum Operations*_ \n", "\n", "The latest version of this notebook is available on https://github.com/QISKit/qiskit-tutorial.\n", "\n", "***\n", "### Contributors\n", - "Rudy Raymond, Ali Javadi" + "Jay Gambetta, Rudy Raymond and Ali Javadi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Quantum Gates \n", - "\n", - "Quantum gates on $q$ qubits can be regarded as unitary operations rotating a complex vector of dimension $2^q$, that corresponds to the quantum state. This tutorial is written to list elementary gates and their corresponding unitary matrices. Each gate is documented in [the OpenQASM language](https://github.com/QISKit/openqasm/blob/master/spec-human/qasm2.pdf). The gates are defined in [the file `qelib1.inc`](https://github.com/QISKit/openqasm/blob/master/examples/generic/qelib1.inc), and implemented in [the standard extension](https://github.com/QISKit/qiskit-sdk-py/tree/master/qiskit/extensions/standard). The gates can be divided into one-qubit gates and multi-qubit gates. \n", - "\n", - "Notice that in the IBM Quantum Experience, the order of qubits are represented from the most significant bit (MSB) on the left to the least significant bit (LSB) on the right. This is similar to bitstring representation on classical computers, and enables easy conversion from bitstrings to integers after measurements are performed. Thus, we write the tensor product of qubits $q_0$, $q_1$, and $q_2$ as $q_2 \\otimes q_1 \\otimes q_0$. The physics community often writes this in the opposite way, and care must be taken when working with these scenarios, as demonstrated in multi-qubit gates below.\n", - "\n", - "We start with preparing the environment. " + "In the first notebook we did not describe the operations just showed you how to make a quantum circuit and run it. Now its time to learn what each of them do. In this notebook we will go into the different operations that are available in QISKit-core. These are:\n", + "* Single-qubit quantum gates\n", + "* Multi-qubit quantum gates\n", + "* Measurements\n", + "* Reset\n", + "* Conditionals\n", + "* State initialization" ] }, { "cell_type": "code", - "execution_count": 96, - "metadata": { - "collapsed": true - }, + "execution_count": 1, + "metadata": {}, "outputs": [], "source": [ "# Checking the version of PYTHON; we only support > 3.5\n", "import sys\n", "if sys.version_info < (3,5):\n", " raise Exception('Please use Python version 3.5 or greater.')\n", - "\n", + " \n", + "try:\n", + " sys.path.append(\"../../\") # go to parent dir\n", + " import Qconfig\n", + " qx_config = {\n", + " \"APItoken\": Qconfig.APItoken,\n", + " \"url\": Qconfig.config['url']}\n", + "except:\n", + " qx_config = {\n", + " \"APItoken\":\"YOUR_TOKEN_HERE\",\n", + " \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ "# Useful additional packages \n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", - "from math import pi\n", - "\n", - "# Importing the QISKit\n", + "from math import pi" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n", "from qiskit import QuantumProgram\n", - "import Qconfig\n", - "\n", - "# Import basic plot tools\n", - "from qiskit.tools.visualization import plot_histogram, plot_state\n", - "\n", - "# Create the quantum program\n", - "Q_program = QuantumProgram()\n", - "Q_program.set_api(Qconfig.APItoken, Qconfig.config[\"url\"])\n", - "\n", - "# Creating registers\n", - "n_qubits = 3\n", - "qr = Q_program.create_quantum_register(\"qr\", n_qubits)\n", - "cr = Q_program.create_classical_register(\"cr\", n_qubits)\n", - "\n", - "demoCircuit = Q_program.create_circuit('demoCircuit', [qr], [cr])" + "from qiskit.backends import discover_local_backends, discover_remote_backends\n", + "from qiskit.tools.visualization import circuit_drawer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## One-Qubit Gates\n", + "## Single Qubit Quantum states\n", "\n", - "The one-qubit gates available consist of Pauli $X, Y, Z$ gates, the Identity gate, primitives, and standard rotation gates. The primitives contain parametrized $u$ matrices (from one up to three parameters), the Hadamard gate, the square-root of $Z$ (also referred as the $S$) gate and its conjugate, the square-root of $S$ (also referred as the $T$) gate and its conjugate. The standard rotation gates are those that define rotations around standard axis. \n", + "A single qubit quantum state can be written as\n", "\n", - "### Pauli gates\n", + "$$|\\psi\\rangle = \\alpha|0\\rangle + \\beta |1\\rangle$$\n", "\n", - "#### $X$: bit-flip gate\n", "\n", - "The bit-flip gate $X$ is defined as:\n", + "where $\\alpha$ and $\\beta$ are complex numbers. In a measurement the probability of the bit being in $|0\\rangle$ is $|\\alpha|^2$ and $|1\\rangle$ is $|\\beta|^2$. As a vector this is\n", "\n", "$$\n", - "X \\equiv u3(\\pi, 0, \\pi) = \n", - "-i\n", - "\\begin{pmatrix}\n", - "0 & 1\\\\\n", - "1 & 0\n", - "\\end{pmatrix}\n", - "\\equiv \n", + "|\\psi\\rangle = \n", "\\begin{pmatrix}\n", - "0 & 1\\\\\n", - "1 & 0\n", - "\\end{pmatrix},\n", + "\\alpha \\\\\n", + "\\beta\n", + "\\end{pmatrix}.\n", "$$\n", - "where in the hereafter $i = \\sqrt{-1}$, and the symbol $\\equiv$ denotes the equivalence up to the global phase. \n", "\n", - "#### $Y$: bit- and phase-flip gate\n", + "Note due to conservation probability $|\\alpha|^2+ |\\beta|^2 = 1$ and since global phase is undetectable $|\\psi\\rangle := e^{i\\delta} |\\psi\\rangle$ we only requires two real numbers to describe a single qubit quantum state.\n", "\n", - "The $Y$ gate is defined as:\n", + "A convenient representation is\n", "\n", - "$$\n", - "Y \\equiv u3(\\pi, \\pi/2, \\pi/2) = \n", - "\\begin{pmatrix}\n", - "0 & -i\\\\\n", - "i & 0\n", - "\\end{pmatrix}\n", - "$$\n", + "$$|\\psi\\rangle = \\cos(\\theta/2)|0\\rangle + \\sin(\\theta/2)e^{i\\phi}|1\\rangle$$\n", "\n", - "#### $Z$: phase-flip gate\n", + "where $0\\leq \\phi < 2\\pi$, and $0\\leq \\theta \\leq \\pi$. From this it is clear that there is a one-to-one correspondence between qubit states ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n", + "\n", + "Quantum gates/operations are usually represented as matrices. A gate which acts on a qubit is represented by a $2\\times 2$ unitary matrix $U$. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.\n", + "\n", + "$$|\\psi'\\rangle = U|\\psi\\rangle$$\n", "\n", - "The $Z$ gate is defined as:\n", + "A general unitary must be able to take the $|0\\rangle$ to the above state. That is \n", "\n", "$$\n", - "Z = u1(\\pi) = \n", - "\\begin{pmatrix}\n", - "1 & 0\\\\\n", - "0 & -1\n", + "U = \\begin{pmatrix}\n", + "\\cos(\\theta/2) & a \\\\\n", + "e^{i\\phi}\\sin(\\theta/2) & b \n", "\\end{pmatrix}\n", + "$$ \n", + "\n", + "where $a$ and $b$ are complex numbers constrained such that $U^\\dagger U = I$ for all $0\\leq\\theta\\leq\\pi$ and $0\\leq \\phi<2\\pi$. This gives 3 constraints and as such $a\\rightarrow -e^{i\\lambda}\\sin(\\theta/2)$ and $b\\rightarrow e^{i\\lambda+i\\phi}\\cos(\\theta/2)$ where $0\\leq \\lambda<2\\pi$ giving \n", + "\n", + "$$\n", + "U = \\begin{pmatrix}\n", + "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n", + "e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2) \n", + "\\end{pmatrix}.\n", "$$\n", "\n", - "The pauli gates can be added as below." + "This is the most general form of a single qubit unitary." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Single-Qubit Gates\n", + "\n", + "The single-qubit gates available are:\n", + "* u gates\n", + "* Identity gate\n", + "* Pauli gates\n", + "* Cliffords gates\n", + "* $C3$ gates\n", + "* Standard rotation gates \n", + "\n", + "We have provided a backend: `local_unitary_simulator` to allow you to calculate the unitary matrices. " ] }, { "cell_type": "code", - "execution_count": 97, + "execution_count": 4, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 97, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "pauli_demo = Q_program.create_circuit('pauli_demo', [qr], [cr])\n", - "pauli_demo.x(qr[0]) # applying x gate to the first qubit\n", - "pauli_demo.y(qr[1]) # applying y gate to the second qubit\n", - "pauli_demo.z(qr[2]) # applying z gate to the third qubit" + "q = QuantumRegister(\"q\", 1)\n", + "c = ClassicalRegister(\"c\", 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can illustrate the effect of each gate on each qubit by looking at how the state vectors get rotated on the Bloch sphere. We see 180 degree rotations of the initial $|0\\rangle$ state (north pole) about the relavent axis in each case." + "### u gates\n", + "\n", + "In QISKit we give you access to the general unitary using the $u3$ gate\n", + "\n", + "$$\n", + "u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda) \n", + "$$\n" ] }, { "cell_type": "code", - "execution_count": 98, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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SGy+fz2NsbAzhcLjCwiQ3qRmYqXdAnDbJZBI9PT1ViRbYm2WrqiqmpqZQLBZx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\ngg==\n", 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RSNJux42pqSk4nU50d3ejvb3dlAf/MFm2jdRIyXUi3Rj02sWTDMCDyEo8LHig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\nGjy4evUqli5div/85z8ICwvj/DiBQYUQbG9VDB0bP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gCMXFxaTOEe9sqhjR0U+dOhUQEPDUU081NzdrVigQCMh2TFXCw8N//vnnEQUUFxdPnTrV19fX399f7adgRrCFaKYg+bcA4F//+teoypXMuskoGQlWr16dkJBQU1Njb28fEBBAnuVaW1u7urpA4/UcsqbV2tqqthxFHgU194l3dHQUFxdrPj2aP/Hx8bGxsRcuXLhy5Qp5K9zf33/BggX6rP+r1TNp0qTq6ur6+nrVOfzIyEgbGxuJREJ1HW1cvnzZUPExMTENDQ3arrq4uOTn59fW1paUlHR1dbm4uJCVKW0bpRYuXEg6w6JFixQKheas2XgLthDNFNQr7GpbMcyB0fObODo6RkZGqp7RlnzMz8+vqqqqqalJzU2uX79uY2OjeTPPzc1lsVhqG7omClZWVi+++CKZ4DAaDofj6ura0tLS2tqq6iZkuvfo0aPHjx+XSCQkZzqTBAUFjTiFrJtR/y3HFQvRfPz4cQDw8fExn2VvCmPywlI3TDU3SUhIAI2XX5qamrq7u+fNm6c5R52dnf3SSy+NU55xc4O6pagilUrJS+WqE9sEMlEnEAjI45iZMzAwoP+WYjNhImru7e0l6cfffPNNU2sZAWPchIxNrKys1PKwx8bGWltb5+TkqG5vJ3suFi9erFbJpUuXGhsbJ8Q2E1p49dVXNTNC7du3b3h4+Omnn9ZMjBQdHU1ShGZmZjIkcQwcPHiQ3EsmEBNR8/79++Vyub29/dg3jo8Lhn6dS6FQkBeTQkNDNa++9957pM7bt2+LxeLPP/+cxWL5+/sPDg6qRSYnJ/P5fIO+qEo7Y/kOsaEcOHCAxWItXbr09OnT/f39vb29mZmZNjY2VlZWVVVVIxahtktevXqVAYVGMzAwEBUVZdo/paFMRM3Ul0O/+OIL/UuZ0ZqOJiQLAQBs2LBB86pcLt+0aZPqTFJgYKDmloqHDx/a29v/5S9/GZP2McOkmyiVysLCQuotBIK3t/eFCxd0FCHLYS+//DIzCo0jJSXl8OHDplZhGBNRM3nPKzg4WC6X61/KjNZ0NNE2aULgcDhff/31pk2bSktLRSJRcHBwbGys6qYVwpEjR0QiUVJSkqGtT2gWL168cOHCCxcuVFVVWVlZzZo1Kzw8XPej+86dO48fP37s2LGjR48uWbKEMan6U1tby+fzExMTTS3EACai5sbGxo8++ojNZu/du9e0M8e6MHRsIpPJRCKRSCQyyCDViIiImDt3rtHF6YLhsYlxnDp1isvl8vn8lpYWU2tBTINYLCYf5dq1a5ehZRn9DrG3t7dBSZa4XK6dnZ2dnd1YDLK9vT01NdXo4hZFTEzM/v37u7q64uPjdWSTRR5VlErlmjVrrl69+uc//5nasG+esJTm921kxjh8+PDy5ctbW1unTZtmai2jIJVKAYDL5Wo+NiKPPOSvb9wnq9LS0vLz81taWugWNQIm/nIooifG9STk0WCi/PXxRocgCD2gmyAIQg/oJgiC0AO6CYIg9IBugiAIPaCbIAhCD+gmCILQA+43AaFQqCM/OIJMaEiicmbasmg3IR800cxUhCCPEoxtfrNoN9myZYtcLidJiRDkkUQoFDKWYs6i39NBEIRGcBYWQRB6QDdBEIQe0E0QBKEHdBMEQegB3QRBEHpAN0EQhB7QTRAEoQd0EwRB6AHdBEEQekA3QRCEHtBNEAShB3QTBEHoAd0EQRB6QDdBEIQe0E0QBKGH8XWTe/fuffjhh3PnzvXw8HBycgoMDExISCguLh7XRhEEMQnjlS1JKpV+/PHHn332mVwu17z6wgsvnDt3bjzaRRDEVIxLJseHDx/GxcWVl5cDQFhYWGJiopeX14MHD5qbm/Py8pqbm728vMajXQRBTAj9YxO5XB4VFVVeXm5jY5OVlbVmzRrVqzKZLCMj49lnn509ezZ1RiwWOzk50SsDQRCmUdLN3//+d1Jzfn6+7siampr58+ez2WwA8PLyysrKol0MgiCMQfPY5O7du35+fnK5PD4+vqioSEfktWvXoqKi2Gz2+vXrnZ2dCwoKrl279t57723fvp1GPQiCMAe95vTGG2+QaisqKnSEKRSKoKAgW1vbmpoackYul8+fP5/D4Vy/fp1eSQiCMAOdK8QKheKHH34AgJCQkDlz5uiIrKmpqa2tTUlJCQoKImc4HE56evrw8HB6ejqNkhAEYQw613Tq6+t7e3tBj6/nlZSUAMCCBQtUT4aEhLi5uV28eNG41qurq+Pi4mQymXHFEWYQiUQ8Ho/H45laCKIVqVQql8sN/ZxuZGQknW7S2tpKDvz9/XVHnj59GgACAwPVzvv7+5eXl3d2drq7uxvaupeX1+uvv45uYubcvHnTw8PD2dnZ1EIQrfT29goEglH/i9UIDQ2l003I6gwAjPov3dHRAQCPP/642nlvb+/y8vKmpiYj3MTFxQVncBHEhNA5b/K73/2OHNy4cUN3pFAoZLPZHA5H7bytrS0ADAwM0KgKQRBmoHNsMmPGjMcee6y9vb2wsPDmzZuaXwuvq6u7ePHipk2b+vv7raxGaJqcFIlERrTe2NiYnJwskUiMKIswRktLi7Ozs4ODg6mFIFrp6+sTiUTTpk0zqNTzzz9P85POJ598snbtWrlcHh0d/eWXX0ZFRdnZ2bW1tVVWVh45cqSoqGjjxo0AYGNjIxaLNWsYGhqC30YohmJjY+Pp6Tnia0GI+TA4OOjh4eHi4mJqIYhWenp6BALBE088YVApPp9P83s6q1evzsvLKykp6ejoWLZsmdpVR0fHqKgoAHBycurt7R0aGuJyuaoBUqmUXDWiaU9Pz0OHDhmpG0GQMUNzRgIWi1VYWPjBBx+oTdoHBATs2LGjpaXllVdegd/8gloDorh//z4AODo60qsKQRAGGK+MBENDQ2T7iaOjo5eXF5/PV726cuXKQ4cOlZSUqG054fP5/f39vb29hq51IwhicsYrWxKXyw0NDY2JiZkzZ46alQBAQkICAFRUVKiebGpq6u7unjdvHloJgkxETJPJMTY21traOicnZ3BwkDr51VdfAcDixYtNIglBkDFiGjdxcHD461//eu/evWXLlt25c2dwcHDXrl0ZGRn+/v5q+VAQBJkojNe8yagMDw+/9dZbmZmZlIDAwMDCwkJvb2+T6EEQZIyYzE0IDQ0NpaWlIpEoODg4NjaW2puPIMiE4/8AaM+1hRUDcJgAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, + "execution_count": 5, "metadata": {}, - "output_type": "display_data" - }, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.u3(pi/2,pi/2,pi/2,q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ { "data": { - "image/png": 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4GKFQqMzCJDepGZipd0CcNolEAt3d3RWJFtieZauqKsbHx1EoFHDu3LmyCIqd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\nrFy5Ej/88AMcHR0hkUiQlJSEw4cPw8HBoV8pFIQQ5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"text/plain": [ - "" + "array([[ 0.707+0.j , -0. -0.707j],\n", + " [ 0. +0.707j, -0.707+0.j ]])" ] }, + "execution_count": 6, "metadata": {}, - "output_type": "display_data" + "output_type": "execute_result" } ], "source": [ - "circuits = ['pauli_demo']\n", - "result = Q_program.execute(circuits, backend='local_unitary_simulator', shots=1024)\n", - "ground = np.zeros(2**n_qubits)\n", - "ground[0]=1.0\n", - "state_pauli = np.dot(result.get_data('pauli_demo')['unitary'],ground)\n", - "rho_pauli = np.outer(state_pauli, state_pauli.conj())\n", - "plot_state(rho_pauli,'bloch')" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Identity gate\n", - "\n", - "The identity gate does nothing (but can add noise in the real device).\n", + "The $u2(\\phi, \\lambda) =u3(\\pi/2, \\phi, \\lambda)$ has the martix form\n", "\n", "$$\n", - "I = \n", - "\\begin{pmatrix}\n", - "1 & 0 \\\\\n", - "0 & 1\n", + "u2(\\phi, \\lambda) = \n", + "\\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n", + "1 & -e^{i\\lambda} \\\\\n", + "e^{i\\phi} & e^{i(\\phi + \\lambda)}\n", "\\end{pmatrix}.\n", "$$\n", "\n", - "It can be used in a circuit like below. Note the difference between results when running on an ideal simulator versus running on a real device." + "This is a useful gate as it allows us to create superpositions" ] }, { "cell_type": "code", - "execution_count": 118, + "execution_count": 7, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Counts from ideal simulation of identity gates: {\"000\": 1024}\n" - ] + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "import json\n", - "identity_demo = Q_program.create_circuit('identity_demo', [qr], [cr])\n", - "\n", - "# applying iden gate to the first qubit\n", - "# barriers prevent them from being optimized away\n", - "identity_demo.iden(qr[0])\n", - "identity_demo.barrier(qr[0])\n", - "identity_demo.iden(qr[0])\n", - "identity_demo.barrier(qr[0])\n", - "identity_demo.iden(qr[0])\n", - "identity_demo.barrier(qr[0])\n", - "identity_demo.measure(qr[0], cr[0])\n", - "\n", - "circuits = ['identity_demo']\n", - "result_ideal = Q_program.execute(circuits, backend='local_qasm_simulator', shots=1024)\n", - "result_noisy = Q_program.execute(circuits, backend='ibmqx2', shots=1024, timeout=300)\n", - "\n", - "counts_ideal = result_ideal.get_counts('identity_demo')\n", - "counts_noisy = result_noisy.get_counts('identity_demo')\n", - "print(\"Counts from ideal simulation of identity gates: {}\".format(\n", - " json.dumps(counts_ideal)))\n", - "print(\"Counts from a real run of identity gates (i.e. wait): {}\".format(\n", - " json.dumps(counts_noisy)))" + "qc = QuantumCircuit(q, c)\n", + "qc.u2(pi/2,pi/2,q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.707+0.j , -0. -0.707j],\n", + " [ 0. +0.707j, -0.707+0.j ]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Primitives\n", - "\n", - "The primitives contain parametrized $u$ matrices (from one up to three parameters), the Hadamard gate, the square-root of $Z$ (also referred as the $S$) gate and its conjugate, the square-root of $S$ (also referred as the $T$) gate and its conjugate. \n", - "\n", - "#### u3 (or, U gates with three parameters)\n", - "\n", - "$u3(\\theta, \\phi, \\lambda$ (or, $U(\\theta, \\phi, \\lambda)$) gates are rotations of 1-qubit state whose mathematical definition are:\n", + "The $u1(\\lambda)= u3(0, 0, \\lambda)$ gate has the matrix form\n", "\n", "$$\n", - "u3(\\theta, \\phi, \\lambda) = \n", + "u1(\\lambda) = \n", "\\begin{pmatrix}\n", - "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2)\\\\\n", - "e^{i\\phi}\\sin(\\theta/2) & e^{i(\\phi + \\lambda)}\\cos(\\theta/2)\n", - "\\end{pmatrix}.\n", + "1 & 0 \\\\\n", + "0 & e^{i \\lambda}\n", + "\\end{pmatrix},\n", "$$\n", "\n", - "Notice that the above unitaries are essentially equivalent to $e^{-i{(\\phi + \\lambda)}/{2}} u3(\\theta, \\phi, \\lambda)$, as in Eq.(2) of the openqasm [here](https://github.com/QISKit/openqasm/blob/master/spec-human/qasm2.pdf). \n", - "\n", - "Here is the command to add such a $u3$ gate to a circuit. " + "which is a useful as it allows us to apply a quantum phase." ] }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { + "image/png": "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\n", "text/plain": [ - "" + "" ] }, - "execution_count": 100, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "theta = pi/2.0 \n", - "phi = pi/3.0\n", - "lambd = pi/4.0\n", - "demoCircuit.u3(theta, phi, lambd, qr[0]) #applying a u3 gate to the first qubit " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "#### u2 (or, U gates with two parameters)\n", - "\n", - "$u2(\\phi, \\lambda)$ gates are rotations of 1-qubit state whose mathematical definitions are:\n", - "\n", - "$$\n", - "u2(\\phi, \\lambda) \\equiv u3(\\pi/2, \\phi, \\lambda) = \n", - "\\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n", - "1 & -e^{i\\lambda} \\\\\n", - "e^{i\\phi} & e^{i(\\phi + \\lambda)}\n", - "\\end{pmatrix}.\n", - "$$\n", - "\n", - "We can add a $u2$ gate to a circuit as follows." + "qc = QuantumCircuit(q, c)\n", + "qc.u1(pi/2,q)\n", + "circuit_drawer(qc)" ] }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "array([[1.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+1.j]])" ] }, - "execution_count": 101, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "phi = pi/3.0\n", - "lambd = pi/4.0\n", - "demoCircuit.u2(phi, lambd, qr[0]) #applying a u2 gate to the first qubit " + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#### u1 (or, U gates with one parameter)\n", - "\n", - "$u1(\\lambda)$ gates are rotations of 1-qubit state whose mathematical definitions are:\n", + "The $u0(\\delta)= u3(0, 0, 0)$ gate is the identity matrix. It has the matrix form\n", "\n", "$$\n", - "u1(\\lambda) = u3(0, 0, \\lambda) = \n", + "u0(\\delta) = \n", "\\begin{pmatrix}\n", "1 & 0 \\\\\n", - "0 & e^{i \\lambda}\n", + "0 & 1\n", "\\end{pmatrix}.\n", "$$\n", "\n", - "We can add a $u1$ gate to a circuit as below." + "The identity gate does nothing (but can add noise in the real device for a period of time equal to fractions of the single qubit gate time)" ] }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 11, "metadata": {}, "outputs": [ { "data": { + "image/png": "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\n", "text/plain": [ - "" + "" ] }, - "execution_count": 102, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "lambd = pi/4.0\n", - "demoCircuit.u1(lambd, qr[0]) #applying a u1 gate to the first qubit " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "#### Hadamard gate (Clifford)\n", - "\n", - "$$\n", - "H = u2(0, \\pi) =\n", - "1/\\sqrt{2}\n", - "\\begin{pmatrix}\n", - "1 & 1\\\\\n", - "1 & -1\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "#### $S$ (or, $\\sqrt{Z}$ phase) gate (Clifford)\n", - "\n", - "$$\n", - "S = u1(\\pi/2) = \n", - "\\begin{pmatrix}\n", - "1 & 0\\\\\n", - "0 & e^{i\\pi/2}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "#### $S^{\\dagger}$ (or, conjugate of $\\sqrt{Z}$ phase) gate (Clifford)\n", - "\n", - "$$\n", - "S^{\\dagger} = u1(-\\pi/2) = \n", - "\\begin{pmatrix}\n", - "1 & 0\\\\\n", - "0 & e^{-i\\pi/2}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "The above Clifford gates can be added as below." + "qc = QuantumCircuit(q, c)\n", + "qc.u0(pi/2,q)\n", + "circuit_drawer(qc)" ] }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "array([[1.+0.j, 0.+0.j],\n", + " [0.+0.j, 1.+0.j]])" ] }, - "execution_count": 103, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "demoCircuit.h(qr[0]) #applying h gate to the first qubit\n", - "demoCircuit.s(qr[0]) #applying s gate to the first qubit\n", - "demoCircuit.sdg(qr[0]) #applying sdg gate to the first qubit" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#### $T$ (or, $\\sqrt{S}$ phase) gate ($C3$ gate)\n", - "\n", - "$$\n", - "T = u1(pi/4) = \n", - "\\begin{pmatrix}\n", - "1 & 0\\\\\n", - "0 & e^{i \\pi/4}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "#### $T^{\\dagger}$ (or, conjugate of $\\sqrt{S}$ phase) gate ($C3$ gate)\n", - "\n", - "$$\n", - "T^{\\dagger} = u1(-pi/4) = \n", - "\\begin{pmatrix}\n", - "1 & 0\\\\\n", - "0 & e^{-i \\pi/4}\n", - "\\end{pmatrix}\n", - "$$\n", + "### Identity gate\n", "\n", - "They can be added as below." + "The identity gate is $Id = u0(1)$." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.iden(q)\n", + "circuit_drawer(qc)" ] }, { "cell_type": "code", - "execution_count": 104, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "array([[1.+0.j, 0.+0.j],\n", + " [0.+0.j, 1.+0.j]])" ] }, - "execution_count": 104, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "demoCircuit.t(qr[0]) #applying t gate to the first qubit\n", - "demoCircuit.tdg(qr[0]) #applying tdg gate to the first qubit" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Standard Rotations\n", - "\n", - "The standard rotation gates are those that define rotations around the standard axis. \n", - "\n", - "#### Rotation around X-axis\n", - "\n", - "$$\n", - "R_x(\\theta) = u3(\\theta, -\\pi/2, \\pi/2) \\equiv \n", - "\\begin{pmatrix}\n", - "\\cos(\\theta/2) & -i\\sin(\\theta/2)\\\\\n", - "-i\\sin(\\theta/2) & \\cos(\\theta/2).\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "#### Rotation round Y-axis\n", + "### Pauli gates\n", "\n", - "$$\n", - "R_y(\\theta) = u3(\\theta, 0, 0) \\equiv\n", - "\\begin{pmatrix}\n", - "\\cos(\\theta/2) & \\sin(\\theta/2)\\\\\n", - "\\sin(\\theta/2) & \\cos(\\theta/2).\n", - "\\end{pmatrix}\n", - "$$\n", + "#### $X$: bit-flip gate\n", "\n", - "#### Rotation around Z-axis\n", + "The bit-flip gate $X$ is defined as:\n", "\n", "$$\n", - "R_z(\\phi) = u1(\\phi) = \n", + "X = \n", "\\begin{pmatrix}\n", - "1 & 0 \\\\\n", - "0 & e^{i \\phi}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "They can be added as below." + "0 & 1\\\\\n", + "1 & 0\n", + "\\end{pmatrix}= u3(\\pi,0,\\pi)\n", + "$$" ] }, { "cell_type": "code", - "execution_count": 105, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { + "image/png": "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\n", "text/plain": [ - "" + "" ] }, - "execution_count": 105, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "theta = pi/4\n", - "phi = pi/4\n", - "demoCircuit.rx(theta, qr[0]) #applying rotation around x-axis gate to the first qubit\n", - "demoCircuit.ry(theta, qr[0]) #applying rotation around y-axis gate to the first qubit\n", - "demoCircuit.rz(phi, qr[0]) #applying rotation around z-axis gate to the first qubit" + "qc = QuantumCircuit(q, c)\n", + "qc.x(q)\n", + "circuit_drawer(qc)" ] }, { - "cell_type": "markdown", + "cell_type": "code", + "execution_count": 16, "metadata": {}, - "source": [ - "## Multi-Qubit Gates\n", - "\n", - "The standard multi-qubit gates consist of two-qubit gates and three-qubit gates. The two-qubit gates consist of the controlled Pauli gates, the controlled Hadamard gate, the controlled rotation gates, and the swap gate. The three-qubit gates consist of the Toffoli gate and the Fredkin gate. \n", - "\n", - "### Controlled Pauli Gates\n", - "\n", - "#### Controlled-X (or, controlled-NOT) gate\n", + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.+0.j, 1.-0.j],\n", + " [ 1.+0.j, -0.+0.j]])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'],3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### $Y$: bit- and phase-flip gate\n", + "\n", + "The $Y$ gate is defined as:\n", + "\n", + "$$\n", + "Y = \n", + "\\begin{pmatrix}\n", + "0 & -i\\\\\n", + "i & 0\n", + "\\end{pmatrix}=u3(\\pi,\\pi/2,\\pi/2)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.y(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.+0.j, -0.-1.j],\n", + " [ 0.+1.j, -0.+0.j]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'],3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### $Z$: phase-flip gate\n", + "\n", + "The phase flip gate $Z$ is defined as:\n", + "\n", + "$$\n", + "Z = \n", + "\\begin{pmatrix}\n", + "1 & 0\\\\\n", + "0 & -1\n", + "\\end{pmatrix}=u1(\\pi)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.z(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.+0.j, 0.+0.j],\n", + " [ 0.+0.j, -1.+0.j]])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'],3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Clifford gates\n", + "\n", + "#### Hadamard gate\n", + "\n", + "$$\n", + "H = \n", + "\\frac{1}{\\sqrt{2}}\n", + "\\begin{pmatrix}\n", + "1 & 1\\\\\n", + "1 & -1\n", + "\\end{pmatrix}= u2(0,\\pi)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.h(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.707+0.j, 0.707-0.j],\n", + " [ 0.707+0.j, -0.707+0.j]])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### $S$ (or, $\\sqrt{Z}$ phase) gate\n", + "\n", + "$$\n", + "S = \n", + "\\begin{pmatrix}\n", + "1 & 0\\\\\n", + "0 & i\n", + "\\end{pmatrix}= u1(\\pi/2)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.s(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+1.j]])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### $S^{\\dagger}$ (or, conjugate of $\\sqrt{Z}$ phase) gate\n", + "\n", + "$$\n", + "S^{\\dagger} = \n", + "\\begin{pmatrix}\n", + "1 & 0\\\\\n", + "0 & -i\n", + "\\end{pmatrix}= u1(-\\pi/2)\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAABZCAIAAADHO+MmAAAOsklEQVR4nO2da1ATVxvHT0KAREID4RJAaAGxRDqICUUqLRUsUFELI8jUwkANdVotYx2pndGOjhWtI6NSVLS0HwLqSCmI1JZBays4U2gtlxKUUAsFoYRLBaXhkpALm/fDmdnkzWVJYtiN4/4+hd1z9nmy/HPOc+4UjUYDnlUKCgqOHz/u6+tLtCNYyOVymUw2OTlJoVAW2xZtsQ3YM7OzswqFIiMjg2hHsGhra7t16xaCIA4ODott65lWg4eHB5VKPX78ONGOYHH69Olbt27hY4uKjxmSpwJSDSRaSDWQaCHVQKKFqlarlUolzlYVCgXOFknMgbpz5853330XZ6uBgYHnz5/H2SjJglDHxsbGxsZwtsrn88+ePYuzUZIFISZuEAgE9+/fv3PnDiHWSUxBjBpSUlI8PDyEQiEh1gnk0aNHsbGxdvszIEYNTk5OWVlZ3377rUwmI8QBohgcHGxqampvbyfaEeMQ1sLMzc2dmpqqqakhygFCgCNkdjtORpgaIiIieDxeWVkZUQ4QAofDodFopBqMkJube/v27QcPHhDoA85QqVQfHx8/Pz+iHTEOkWOYmZmZe/fuLS8vP3z4MIFuPAkKhaKhoeHXX38dGRmh0WjLli1btmxZTEwMxq/fz8/PbssGItXAZrNTU1PLy8sPHTpEpT5lfeQymay4uPjEiRP//fef3i1nZ+ft27fv27fP398fXmlsbDx79mxYWBifz/fx8WloaGhraxOJRElJSe+//z7erpuG4PkNAoGgqqqqoaEhISGBWE8soqenJy0tTSwWwz85HA6Xy5XJZF1dXXK5XKFQnDt3TiKRfPfddzDB4OBga2vr9PS0UqkcHx9vaWnp6OgQiUQBAQGEfQejbNq0KS4uTrMQCIL8+OOP2dnZUVFRb7zxxv79+0dGRjQazccff8zlcsPCwubm5hZ8iCHz8/P+/v6ZmZlW5H1yCgsLaTSapbl6e3u9vLwAAA4ODh999NHw8DB6S6VSffPNN8uXLwcA1NbWGs2+cuVKmUxmvrni4mIAgFqtttRPKzBLDRKJJC4uTk9GLBarsbExNDQUABAeHm61B59++imdTp+cnLT6CVZjhRoUCgWXywUAMBiM3377zWiaycnJLVu2qFQqo3cZDEZ3d7f5FvFUw8K1dV9fX1RU1O3btwEAS5YsyczMPHr06Pbt22dmZjZv3tzT0wMAWL16tdWFk0AgmJubq6ystPoJePLFF1/cv38fAPDll1++8sorRtO4ublVV1fTaEZqYalUKpfLR0dHF9dLa1kgbpBKpQkJCdD72NjYqqoqHx8feGvdunWZmZnwc3R0tNUehISExMbGCoXCHTt2WP0QfNBoNKWlpQAAb29v6wZ+Hz58CACwWzUsUDbs3r17YGAAAPDee+81NDSgUgAAbN26NTg4GH42LBuUSqVhsG2K3Nzc1tbWrq4uM9MTRV9fH3wbr776qnVPePToEQBgYmLChl7ZECw13L1798KFCwCA5cuXnzt3Tq/oo1AoISEhAAAGg/HSSy+h1zs7O5OSkhgMhru7e1BQ0FdffbWgExkZGUwm0/77JUdGRuCHmZkZ654A36Gjo6PNfLIpWDXFyZMn4YfS0lJnZ2fDBN3d3QCAyMhIVCjt7e3x8fFUKjU/P9/d3f3q1as7duwYHh4uKCjAMOTi4pKRkVFRUXHy5Emr15BMTU399NNPCIKYn+Xu3bsaSxYXwcYCAKCxsbG7uzssLMwyFwGAr5FOp5ufBc4Tu3LlivldMnK5fGho6MUXX7TIN19fX5NtCrVazWKxAACrVq0yGn9KJBL4lPz8fHgFQZCIiAgGgyESidCHJCYmOjg4dHV1YUezWVlZAQEBVgfDGo3m4sWLFn15FIusLF26FH13NTU1phoOpoBBd0VFhflZcJuZ5uXlZbJsaGtrk0qlAID4+HijCdBBejRoEIlEnZ2du3btioiIgFccHBwKCwv5fH5hYSHGf0sqlV69ejU/P9+6rwHJzs6Oi4tTqVTmZ/n6669PnTplkZUjR47k5uYCAEZHR9PT093d3Tds2JCenr5+/XoGg7FgdivKBh6Pd+HChZ6eHovWWikUCqPFOQaenp4m1TA4OAg/mBpiQdWANihu3LgBAHjzzTd1k/F4PC8vr19++QXDj8rKSrlcvm3bNnMdN4GlXXtsNttSEwKBoKOjA53GNzk5efny5cuXL7u4uAgEgsLCwiVLlmBkhzowRzd6BAcH47DyzmRVBKNfAMDk5KTRBFANXl5egYGB8MrPP/8MAAgPD9dLGRoaOjAwgDH7UigUrl27Fsak9s+ZM2d++OGHmJgY3Yp8dna2pKSEz+djtx6hDiwqG/DEpBpg5ysAoLOz0/CuRCJpaWkB/9+2hC8CrVlRgoKCAAC9vb1GDYnF4paWFlj8Pi1s2rSpubl5dHRUKBSmpKSgZfJff/2Vl5eHkdHV1ZVGozGZTFzctBiTakDj5/r6epFIpHtLJpMJBAK4CkNXDVKplEqlGhZo8AcxOztr1JBQKHR1dd2yZYs17hOKt7e3QCC4du1af39/SkoKvFhbW9va2oqRi81me3h44OKgxZhUQ0RExMqVKwEAGo0mOTm5vr5eoVA8fvy4trY2OjoaVgrg/9UwNTVltDsWXjTaRlepVJcuXdq6dSt2dWvn+Pn5VVVV8fl8+GdjYyNGYjabbUW8gg9YTdjPPvsMVo1jY2MbN250dXX19PRMS0tjMplod1NUVBSank6nq9Vqw+fAON9o6FRXVzc+Pv50VRNGcXZ2RveBgN3PpuBwOM899xwuTlkMlho2b95cVlaG/mrVajWPxxMKhc3NzbBvNSQkRLfQc3NzQxDEsI0H+0/c3NwMTQiFQi6Xa2r45+kCrVvRkMsoBQUFOOzSYh0LjFrl5OSkpqaKRCImk8nlcl1cXAAAQ0ND//77LzAYnoD/76GhIXT8AgL7qWBfli6jo6PXr1+38800zAeNrmANa4rXX38dD2+sYuHOThaLtXbt2sjISCgFAABsTQADNcCuUMO2Q1dXF51Ohy0LXS5evEihULKzs61z3a5AEKS+vh4AwGazn655XLpYMxsRjZn11JCamgp0eqUgvb29Dx8+XLduHSomFKFQuHHjRg6HY4UPeDIxMbHgGuKioqI//vgDALBv3z67HZRaEGvUAMsGGo3G4/F0rycnJzs7O5eVlcnlcvTimTNnAABoAwylubm5p6fnqYgfy8vL8/Ly9uzZY2ro8tKlSwcOHAAA8Hi83bt34+udTTFzXiQKgiAwJObz+YZ3Dx48CJ/Z19cnk8lOnTpFoVBCQ0PlcrleytzcXA6HY+moj20xZyYcgiBoeOjr63vkyBGxWDw/Pw/vdnR0pKenw7sBAQESicTmTtrdvEhd4Cg2AGDnzp2Gd9VqdV5enm7MHB4e3t/fr5dsenqayWR+8sknT+T7E2OmGoqKivT6kmk0mo+Pj24fSXR0NJw2bHPsa16kHqaCBoiDg0NJSYlYLC4uLj569GhdXZ1IJDKMH6urq2dmZgQCgaXW8YdCoezZs0csFufl5aE9ymq1emxsDC4pXrp06fnz55ubm+12zYz5WLye4p133oFlI8bQy4oVK1asWIHxkLKysjVr1mCnsSuCg4NLSkqKiop+//339vb28fFxpVLp5+e3evXqmJgYu+0/sBRaUFCQRfO6HB0dnzxmHhkZOXr06BM+BH+cnJxiY2NjY2OJdmSxoMGYH2f+/vtv/I2SLMhTtvqRZFEh1UCihVQDiRZSDSRaSDWQaCHVQKLlmT6t5MGDB/Pz8y+//DLRjmCBPZPKtjzTakhMTGxubtabm2NveHp6+vv747CYAgBA0TzDp5yR6EHGDSRaSDWQaCHVQKKFVAOJFlINJFpINZBoIdVAooVUA4kWUg0kWkg1kGgh1UCihVQDiRZSDSRaFlcNg4ODhw8fXrNmja+vr5ubW3h4eGpq6vXr1xfVKIn1LNKKvrm5uQMHDhjdBgoAYNHKTxLcWJTZLtPT0xs2bGhqagIAREVFZWRkBAYGPn78eGBgoLKycmBgAN1iksS+sLm+VCrVa6+9BgCg0+nl5eV6dxUKBVzNqHuFkINrSAyxvRr2798PdXblyhXslCKRKDExEW47FxgYWFpaanNnSCzCxmro7++HscJbb72FnbKtrc3V1ZXFYu3du/fzzz+PjIwEABw8eNC2/pBYhI3V8MEHH8CC4c6dOxjJnuTsApLFw5azZBEE4XA4ExMTPB4Pbollio6ODj6fv2vXLt0V4vBidna2dSdNzMzM3Lx5c35+3oq8NmRgYMDb25vYrXEVCsXw8LClc8EDAgJsWTagGyZmZ2djpzx27BgAoK6uTu863NHeOuvl5eW2fqvPFljnU1jB0NAQ/AAPycQA4+yCpqamsbEx3ePUzCQnJycuLo7wsmF2dpbBYBB7ELRGo5mdnbV0p3t3d3dbqgF9BXB7egwwzi5oamrq7e21Qg0UCuWFF16wNBeJLrZUA7qPE3rAtCmsO7sAGwRB7t27Z3TbczyRSqVMJhOfpVGmQBBkamrK6MbeGPj6+toybpifn4fHHtFoNLFYbJigs7OzpKREo9EwmUwnJyfDBB9++CEAoLq62grr9n+Aop3DZrNtXFMcO3Zs27ZtarU6ISHh9OnT8fHxLi4uw8PDLS0t1dXV33//Pfx/0+l0uL2eHhhnFyzI22+//fzzz1t0AuJiIJFIPD09iT2rSKlUjo6OWlpv+vj42Li/AUGQ9evXm7LHYrFqamo0Gg08wkqpVOplz8nJAQA0NTXZ1isSM7Fx6EuhUK5du3bo0CF3d3fd61wu98SJE//8809aWhrQObtAL7upswtI8GGx1mirVKp79+5NTEywWKzAwEC9jeazsrIqKipu3Lihd1wih8OZmpqamJgw3LCeBAcWq1ns6OjI5/OTkpKio6MNzxyw9OwCEnwgppPEorMLSPCDqIDF/LMLSHCDMDWYeXYBCZ4QvNPPn3/+efPmzZmZmVWrViUnJxPbvU/yP/g1s/Omq811AAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.sdg(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.-1.j]])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### $C3$ gates\n", + "#### $T$ (or, $\\sqrt{S}$ phase) gate\n", + "\n", + "$$\n", + "T = \n", + "\\begin{pmatrix}\n", + "1 & 0\\\\\n", + "0 & e^{i \\pi/4}\n", + "\\end{pmatrix}= u1(\\pi/4) \n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.t(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1. +0.j , 0. +0.j ],\n", + " [0. +0.j , 0.707+0.707j]])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### $T^{\\dagger}$ (or, conjugate of $\\sqrt{S}$ phase) gate\n", + "\n", + "$$\n", + "T^{\\dagger} = \n", + "\\begin{pmatrix}\n", + "1 & 0\\\\\n", + "0 & e^{-i \\pi/4}\n", + "\\end{pmatrix}= u1(-pi/4)\n", + "$$\n", + "\n", + "They can be added as below." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.tdg(q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1. +0.j , 0. +0.j ],\n", + " [0. +0.j , 0.707-0.707j]])" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Standard Rotations\n", + "\n", + "The standard rotation gates are those that define rotations around the Paulis $P=\\{X,Y,Z\\}$. They are defined as \n", + "\n", + "$$ R_P(\\theta) = \\exp(-i \\theta P/2) = \\cos(\\theta/2)I -i \\sin(\\theta/2)P$$\n", + "\n", + "#### Rotation around X-axis\n", + "\n", + "$$\n", + "R_x(\\theta) = \n", + "\\begin{pmatrix}\n", + "\\cos(\\theta/2) & -i\\sin(\\theta/2)\\\\\n", + "-i\\sin(\\theta/2) & \\cos(\\theta/2)\n", + "\\end{pmatrix} = u3(\\theta, -\\pi/2,\\pi/2)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+/DkqiKWSNQIFdqrAHvmpU6dEj6Mpijk5OWL2Q4cONTQ0lNyW5OjRo7q6ur1u8aEaFN51SDHS0tJ0dHRWr14NALGxsfjGCxcuBAArK6vOzk7VhNdP0LpPJycnGe01pcUiDayCEavLg4ODQWS0CFFdXd3c3Ozj4yPZN09NTf3666/lWiv+3yU5OTkiIiIhIeHSpUuzZs2KjY2VllpFoBYFi8VSbKMLFdPS0oKWY2vo9GkF6nI05q+rqytWzbS2thoYGIwePZrD4WAH0Yaokl0xtI1gZmamwl/Q/qOyuvzMmTMAcOTIEfRnUVERiUTy8fHBuUQgEKCF9FOnTlVBhP0E7TpkYmLy8eNHGS/RlBxLrwgEApQs8/T0lDy7d+9e9M2pqanhcDgnTpwgkUhUKlXyZ3ft2rW2trZy7ayndFSj8uPHjwPAzp07RQ+i1t3FixdxLsSGIdGSao0F20Hu5MmTsl+l0SrHlnOvX79e8iyPx9u4caNoT4VGo9XW1oqZtbW1mZiY/PDDD/2Kvd+oQOWxsbEAEB0dLXacwWAYGhpaW1uLpmIlQXnJBQsWDGSM/QWNarm7u4vtGomPRqscrasAgLS0NGk2FRUVp06dio2NzcrK4vP5kgapqakAUFFRoUDESkTFvU8FaG5uRvsKZWRkqDuW3qmqqjI0NCSTyU+fPpXrQo1WOZfLbW9vb29vl+uLK4aXl9eMGTMUvlxZaL7KhULhb7/9pqenZ2trW1dXp+5YxOFwOGizoYSEBHmvVWmOxdHRUa4Jvnp6esbGxsbGxv1ZKNDY2IgzJkIgir+///nz55uamoKCglT/1hAchELhmjVrnj179v333yu2IYfKIAk1b+9GlREVFfXo0SO0+YmGg8aP9fT0lPs6l36ColJsK56srKygoKCqqipsAcfAIdOuQwRqRzElDTSaGZUkGlQxEBAMEITKCbQfQuUE2g+hcgLth1A5gfZDqJxA+yFUTqD9DOp8uVAo5PP50jacIRhQVDmOO6hV/ueff75588bS0lLdgQxeVKP1Qa3ylJSUvLw8Vb7ygQCDz+czGAxsy4ABZVDPYyEYJBC9TwLth1A5gfZDqJxA+yFUTqD9ECon0H4IlRNoP4TKCbQfQuUE2g+hcgLth1A5gfZDqJxA+yFUTqD9ECon0H4IlRNoP4TKCbSfgVX5u3fvDhw4MGPGjGHDhpmbm9NotODg4Ozs7AF1SkAgxkCtouju7o6NjT169CiPx5M8O2fOnF5fH0xAMBAMyIq4tra2wMBA9OagKVOmhISEODg4fPr0icFgpKenMxgMBweHgfBLQNAryq/LeTyet7d3fn6+oaEhnU5fs2aN6Fkul5uYmDhz5kzs/XJcLpfD4fT6zlsCAuWg9H3/d+7cie5848YNfMvi4mI/Pz+0IbeDg4Pke+QICJSCklVeW1urq6sLAEFBQfiWz58/p1AoZmZm27ZtO3z48KRJkwBg7969yo2HgECodJVHRkaiirywsBDHTCAQuLm5GRkZFRcXoyM8Hs/Pz09HR6e8vFy5IREQKFPlfD7f2toaADw8PPAtX758CQCbN2+WPLh69WolhkRAIBQKlZljKSsra2lpAQBXV1d8y5ycHACYO3eu6EEPDw8bG5vHjx8r5j0xMRG9U3fw0N7erq+vr6+vr+5AVASfz+/o6KBQKKIvlO0Tc3NzZar8/fv3qEClUvEt8/LyAIBGo4kdp1Kp+fn5TCbTzs5OXu8zZ86MjIwUDqZNlCoqKoYNG4ZeCDoY6O7uLi8v9/T0lEvlFhYWylQ59voyLpeLb/nhwwcAGDFihNhxR0fH/Pz86upqBVTu7u7u7u4u71UEgwFljvCPGzcOFV69eoVvyWazyWSy5BtDjYyMAKCjo0OJUREQKLMuHz169PDhwxsbGzMzMysqKsaPHy9mUFpa+vjx440bN7a2tqKEo3g0urqg6D6o169fj4uLEwgEClz7H6Wurs7CwoJCoag7EBXB5XLr6+sdHBzkeumplZWVklssR44cCQsL4/F4vr6+p0+f9vb2NjY2bmhoKCoqun79+q1btzZs2AAAhoaGHA5H8g49PT3wT40uL2ZmZoNt4kBnZ+ewYcMGz87UXV1dHA7H0dFRrveGm5qaKjlfLhAI5s2bJ82fmZnZzZs3hUKhs7MzAHC5XLHLQ0NDASA/P1+5UREMcpQ885ZEImVmZu7fv1+s4+/i4hIXF1dXV7do0SIAQLNWsJwMRn19PfoyKDcqgkHOQM287enpQelz1JCwtbUVPbty5corV67k5OSIpcxtbW1bW1tbWlqMjY0HIiqCwclAraLQ09Pz9PT09/efNm2amMQBIDg4GAAKCwtFD1ZXVzc3N/v4+BASJ1Au6lkRFxAQYGBgkJaW1tnZiR08c+YMAHzzzTdqCYlAi1GPyikUyo8//vju3bslS5bU1tZ2dnYmJCQkJiZSqVSx+egEBP1Hbe8V4vP5W7ZsOXv2LBYAjUbLzMx0dHRUSzwEWoya355VWVmZm5vb3t7u7u4eEBAgV7afgEBG/g93xod/3ZjIHQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.rx(pi/2,q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.707+0.j , -0. -0.707j],\n", + " [ 0. -0.707j, 0.707+0.j ]])" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Rotation round Y-axis\n", + "\n", + "$$\n", + "R_y(\\theta) =\n", + "\\begin{pmatrix}\n", + "\\cos(\\theta/2) & - \\sin(\\theta/2)\\\\\n", + "\\sin(\\theta/2) & \\cos(\\theta/2).\n", + "\\end{pmatrix} =u3(\\theta,0,0)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.ry(pi/2,q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.707+0.j, -0.707+0.j],\n", + " [ 0.707+0.j, 0.707+0.j]])" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Rotation around Z-axis\n", + "\n", + "$$\n", + "R_z(\\phi) = \n", + "\\begin{pmatrix}\n", + "e^{-i \\phi/2} & 0 \\\\\n", + "0 & e^{i \\phi/2}\n", + "\\end{pmatrix}\\equiv u1(\\phi)\n", + "$$\n", + "\n", + "Note here we have used an equivalent as is different to u1 by global phase $e^{-i \\phi/2}$." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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9y46egoICdCCSSu4NdD3y1tjYGI3QwJFWqo0ePbqgoKC8vFxE5aWlpfr6+ijTIkxKSgqFQlm2bJkigX+CCASC8PDw3377LTk5GR/OKREajebr65uZmZmVldXe3q6vr6+yIBHOzs54XUVGUE5p5MiRvXArMkWGzuEFjIjK/f39Qai3CFFeXl5fX+/p6SneNk9KSvryyy/l7cr5RMEw7Kuvvjp79mxiYiJecScA1SiYTKYCq1yonoaGBjQdu3cOn1ZE5ags19HRcXV1FT7v6+urp6eXnJzc1taGnzx+/DgAzJ07V+Qh9+/ff/ny5SeRJu8+GIatXr36zJkzCQkJ4eHhstzi5eWFJtJ/EosDJyYm8ng8Q0PD7ndg9wRy7/eJYRgasTRu3DiRN6mRkdHWrVujo6ODgoKOHTtmaWkZFxcXGxtrb28vvnh0UlKShYUFWt5A44mKikpMTHR0dKyurt69ezeXy8Ur7uvWrZM4J4hCoZw4ccLT0zM/P7+goECV05zlpa2t7ejRowAQHR0t+6AglSLvCnL4dO6IiAjxqzweLyoqSrilQqfTKysrRcxaWloMDQ2//fZbRVNDyqE7q4HKDsFwcwqF8vHjR4J7Ud0GjbXstezfvx8AXFxcRJaMJEaVmUS5y3JplXKEtrb2iRMnoqKicnJy2Gy2i4uLr6+v+MSZ9PR0Npst47v7U8fV1RVTdLmpmJiYrKysS5cuZWZmBgQEKDcwpfDy5cvo6GgtLa2EhASFBxv3OPKW5Vwul81ms9lsuX64Iri7u0+dOlXh25WFasrybvLHH39QqVQLC4vq6mp1xyIKh8NBiw0dOXJE3ntV2itka2srnuMjgEqlGhgYGBgYdOeHW1tbu2HDBoVv71P4+PgkJia+f/9+zpw5qt81hAAMw8LCwh49evTNN98osBqHKqFgvW/tRpVx69Ytb2/voqKiXpjiFQH1H1OpVCXu5dJ9UFSKLcUTFhZWXFz8zz//KDsoCchdLydRC4opqafpnVGJ04sKBhKSHoJUOYnmQ6qcRPMhVU6i+ZAqJ9F8SJWTaD6kykk0HzJfDs3NzdLWnCHpOYQHZvY0fVrlaKqeu7u7ugPpo6hsUd8+rfLg4ODq6moHBwe1LMDZx2EymdLWWlM6fXocC0kfgWx9kmg+pMpJNB9S5SSaD6lyEs2HVDmJ5kOqnETzIVVOovmQKifRfEiVk2g+pMpJNB9S5SSaD6lyEs2HVDmJ5kOqnETzIVVOovn0rMrfvHnzww8/TJ061dLS0sTEhE6n+/v7X79+vUedkpCI0FOzKDo6Ovbt23fw4EEejyd+dfr06RK3DyYh6Ql6ZEZcS0uLn59fXl4eAEycODEwMNDGxqaxsbGqqiotLa2qqsrGxqYn/JKQSET5ZTmPx5sxY0ZeXp6+vn58fLzIjkJcLjc2NnbatGn4VhZcLpfD4Ujc85aERDkofd3/HTt2oCdL234bp7Cw0NvbGy3IbWNjI20/bxKSbqJklVdWVuro6ADAnDlziC0LCgqMjIyMjY23bNmyf//+8ePHA8B3332n3HhISDClq3zNmjWoIH/48CGBmUAgcHZ2ptFohYWF6AyPx/P29tbW1i4tLVVuSCQkylQ5n89H2z2iXdEIQJsDrl+/XvzksmXLlBgSCQmmwE6IBJSUlDQ0NACAk5MTseWNGzcAYObMmcInXV1dzc3Nc3NzFfNeUVHh4eEhvG20xsNms3V1dXV1ddUdiIpob2/n8/niW90T4+/vr0yVv337Fh3Y29sTW966dQsA6HS6yHl7e/u8vDwGg6HAqkuWlparV6/uUyp/9uyZpaWlqampugNREQwGg81m29nZyXXXtGnTlKlyfPsyLpdLbFlXVwcAQ4cOFTlva2ubl5dXXl6ugMoNDAz27Nkj710kfQFl9vCPGTMGHTx9+pTYksViaWlpie8YSqPRAKC1tVWJUZGQKLMsHz58+JAhQ2pray9fvvzs2TNHR0cRg+Li4tzc3KioqObmZpRwFI1GRwcAFNu7taamJjg4uE/9Qqqrq01NTY2MjNQdiIpobGzs6OiwtLSU667Zs2crucZy4MCB5cuX83g8Ly+vY8eOzZgxw8DAoKamJj8/Pz09/cqVK5GRkQCgr6/P4XDEn9DZ2Qn/lujyoqenN2zYMLTPah+hra3N0tLSzMxM3YGoCBqN1traOmLECLnuMjc3V3K+XCAQzJo1S5o/Y2PjixcvYhiGGhBonXZhQkNDASAvL0+5UZH0cZQ88pZCoVy+fHnPnj0iDX8HB4fDhw9XV1fPnz8fANCoFTwng4OWzVfZ4u0kfYSeGnnb2dmJ0ufGxsY2NjYWFhbCV5cuXXru3LkbN26IpMwtLCyam5sbGhrkzYmSkBDQU7MoqFSqm5ubj4/P5MmTRSQOAP7+/gDw8OFD4ZPl5eX19fWenp6kxEmUi3pmxPn6+urp6SUnJwt34hw/fhwA5s6dq5aQSDQY9ajcyMho69atb968CQoKqqysbGtrO3LkSGxsrL29vch4dBKS7qO2fYX4fP7GjRtPnjyJB0Cn0y9fvmxra6uWeEg0GDXvnlVWVpaTk8Nms11cXHx9ffExAiQkSuT/hHWVsgtEeh8AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.rz(pi/2,q)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.707-0.707j, 0. +0.j ],\n", + " [0. +0.j , 0.707+0.707j]])" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(np.exp(-1j*pi/4)*result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note this is different due only to a global phase" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multi-Qubit Gates\n", + "\n", + "The space of quantum computer grows expodential with the number of qubits. For $n$ qubits the complex vector space has dimensions $d=2^n$. \n", + "\n", + "Notice that in the QISKit, the order of qubits are represented from the most significant bit (MSB) on the left to the least significant bit (LSB) on the right (big-endian). This is similar to bitstring representation on classical computers, and enables easy conversion from bitstrings to integers after measurements are performed. That is the first four states of two qubits are $|00\\rangle$, $|01\\rangle$, $|10\\rangle$, and $|11\\rangle$.\n", + "\n", + "The joint space is a tensor product space:\n", + "\\begin{equation}\n", + "\tX\\otimes Y = \n", + "\t\\begin{pmatrix} \n", + "\t\tx_{00} \\begin{pmatrix} \n", + "\t\t\ty_{00} & y_{01} \\\\\n", + "\t\t\ty_{10} & y_{11}\n", + "\t\t\\end{pmatrix} & x_{01} \t\\begin{pmatrix} \n", + "\t\t\t\ty_{00} & y_{01} \\\\\n", + "\t\t\t\ty_{10} & y_{11}\n", + "\t\t\t\\end{pmatrix} \\\\\n", + "\t\tx_{10} \t\\begin{pmatrix} \n", + "\t\t\t\t\ty_{00} & y_{01} \\\\\n", + "\t\t\t\t\ty_{10} & y_{11}\n", + "\t\t\t\t\\end{pmatrix} & x_{11} \t\\begin{pmatrix} \n", + "\t\t\t\t\t\t\ty_{00} & y_{01} \\\\\n", + "\t\t\t\t\t\t\ty_{10} & y_{11}\n", + "\t\t\t\t\t\t\\end{pmatrix}\n", + "\t\\end{pmatrix}\t\t\t\t\t\t\n", + "\\end{equation} which means for the states we have \n", + "\\begin{equation}\\begin{split}\n", + "\t|{00}\\rangle &= \\begin{pmatrix} \n", + "\t\t\\begin{pmatrix} \n", + "\t\t\t1 \\\\\n", + "\t\t\t0\n", + "\t\t\\end{pmatrix} \\\\\n", + "\t\t\\begin{pmatrix} \n", + "\t\t\t0 \\\\\n", + "\t\t\t0 \n", + "\t\t\\end{pmatrix}\n", + "\t\\end{pmatrix} ~ \t|{01}\\rangle = \\begin{pmatrix} \n", + "\t\\begin{pmatrix} \n", + "\t0 \\\\\n", + "\t1\n", + "\t\\end{pmatrix} \\\\\n", + "\t\\begin{pmatrix} \n", + "\t0 \\\\\n", + "\t0 \n", + "\t\\end{pmatrix}\n", + "\t\\end{pmatrix} ~ \t|{10}\\rangle = \\begin{pmatrix} \n", + "\t\\begin{pmatrix} \n", + "\t0 \\\\\n", + "\t0\n", + "\t\\end{pmatrix} \\\\\n", + "\t\\begin{pmatrix} \n", + "\t1 \\\\\n", + "\t0 \n", + "\t\\end{pmatrix}\n", + "\t\\end{pmatrix} ~ \t|{11}\\rangle = \\begin{pmatrix} \n", + "\t\\begin{pmatrix} \n", + "\t0 \\\\\n", + "\t0\n", + "\t\\end{pmatrix} \\\\\n", + "\t\\begin{pmatrix} \n", + "\t0 \\\\\n", + "\t1 \n", + "\t\\end{pmatrix}\n", + "\t\\end{pmatrix}\\end{split}\n", + "\\end{equation}\n", + "\n", + "Thus, we write the tensor product of qubits $q_0$, $q_1$, and $q_2$ as $q_2 \\otimes q_1 \\otimes q_0$. The physics community often writes this in the opposite way, and care must be taken when working with these scenarios, as demonstrated in multi-qubit gates below.\n", + "\n", + "A common two-qubit gate is $C_U$. The $C_U$ when qubit 0 is the control and qubit 1 is the target (eg `cU(q[0],q[1])`) is\n", + "\n", + "\\begin{equation}\n", + "\tC_U = \\begin{pmatrix}\n", + "\t1 & 0 & 0 & 0 \\\\\n", + "\t0 & u_{00} & 0 & u_{01} \\\\\n", + "\t0 & 0 & 1 & 0 \\\\\n", + "\t0 & u_{10} &0 & u_{11}\n", + "\t\t\\end{pmatrix},\n", + "\\end{equation} \n", + "\n", + "\n", + "The $C_U$ when qubit 1 is the control and qubit 0 is the taget (eg `cU(q[1],q[0])`)\n", + "\\begin{equation}\n", + "\tC_U = \\begin{pmatrix}\n", + "\t1 & 0 & 0 & 0 \\\\\n", + "\t0 & 1 & 0 & 0 \\\\\n", + "\t0 & 0 & u_{00} & u_{01} \\\\\n", + "\t0 & 0 & u_{10} & u_{11}\n", + "\t\t\\end{pmatrix}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The standard multi-qubit gates consist of two-qubit gates and three-qubit gates. The two-qubit gates are:\n", + "* controlled Pauli gates\n", + "* controlled Hadamard gate\n", + "* controlled rotation gates\n", + "* controlled phase gate\n", + "* controlled u3 gate\n", + "* swap gate\n", + "\n", + "The three-qubit gates are: \n", + "* Toffoli gate \n", + "* Fredkin gate\n" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "q = QuantumRegister(\"q\", 2)\n", + "c = ClassicalRegister(\"c\", 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Controlled Pauli Gates\n", + "\n", + "#### Controlled-X (or, controlled-NOT) gate\n", "The controlled-not gate flips the `target` qubit when the control qubit is in the state $|1\\rangle$. If we take the MSB as the control qubit (e.g. `cx(q[1],q[0])`), then the matrix would look like\n", "\n", "$$\n", - "C_X = \n", + "C_X = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & 1\\\\\n", + "0 & 0 & 1 & 0\n", + "\\end{pmatrix}. \n", + "$$\n", + "\n", + "However, when the LSB is the control qubit, (e.g. `cx(q[0],q[1])`), this gate is equivalent to the following matrix:\n", + "\n", + "$$\n", + "C_X = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 1\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 1 & 0 & 0\n", + "\\end{pmatrix}. \n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.cx(q[0],q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n", + " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n", + " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Controlled $Y$ gate\n", + "\n", + "Apply the $Y$ gate to the target qubit if the control qubit is the MSB\n", + "\n", + "$$\n", + "C_Y = \n", "\\begin{pmatrix}\n", "1 & 0 & 0 & 0\\\\\n", "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", - "0 & 0 & 1 & 0\n", - "\\end{pmatrix}. \n", + "0 & 0 & 0 & -i\\\\\n", + "0 & 0 & i & 0\n", + "\\end{pmatrix},\n", + "$$\n", + "\n", + "or when the LSB is the control\n", + "\n", + "$$\n", + "C_Y = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & -i\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & i & 0 & 0\n", + "\\end{pmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.cy(q[0],q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+0.j, 0.+0.j, 0.-1.j],\n", + " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j]])" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Controlled $Z$ (or, controlled Phase) gate\n", + "\n", + "Similarly, the controlled Z gate flips the phase of the target qubit if the control qubit is $1$. The matrix looks the same regardless of whether the MSB or LSB is the control qubit:\n", + "\n", + "$$\n", + "C_Z = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 0 & 0 & -1\n", + "\\end{pmatrix}\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.cz(q[0],q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.-0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [ 0.+0.j, 1.-0.j, 0.+0.j, -0.-0.j],\n", + " [ 0.+0.j, 0.+0.j, 1.-0.j, 0.+0.j],\n", + " [ 0.+0.j, -0.+0.j, 0.+0.j, -1.+0.j]])" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Controlled Hadamard gate\n", + "\n", + "Apply $H$ gate to the target qubit if the control qubit is $|1\\rangle$. Below is the case where the control is the LSB qubit.\n", + "\n", + "$$\n", + "C_H = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & \\frac{1}{\\sqrt{2}} & 0 & \\frac{1}{\\sqrt{2}}\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & \\frac{1}{\\sqrt{2}} & 0& -\\frac{1}{\\sqrt{2}}\n", + "\\end{pmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.ch(q[0],q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1. -0.j, 0. +0.j, -0. +0.j, 0. +0.j],\n", + " [ 0. +0.j, 0.707-0.j, 0. +0.j, 0.707-0.j],\n", + " [ 0. -0.j, 0. +0.j, 1. -0.j, 0. +0.j],\n", + " [ 0. +0.j, 0.707-0.j, 0. +0.j, -0.707+0.j]])" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(np.exp(-1j*pi/4)*result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Controlled rotation gates\n", + "\n", + "#### Controlled rotation around Z-axis\n", + "\n", + "Perform rotation around Z-axis on the target qubit if the control qubit (here LSB) is $|1\\rangle$.\n", + "\n", + "$$\n", + "C_{Rz}(\\lambda) = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & e^{-i\\lambda/2} & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 0 & 0 & e^{i\\lambda/2}\n", + "\\end{pmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.crz(pi/2,q[0],q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ],\n", + " [0. +0.j , 0.707-0.707j, 0. +0.j , 0. +0.j ],\n", + " [0. +0.j , 0. +0.j , 1. +0.j , 0. +0.j ],\n", + " [0. +0.j , 0. +0.j , 0. +0.j , 0.707+0.707j]])" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Controlled phase rotation\n", + "\n", + "Perform a phase rotation if both qubits are in the $|11\\rangle$ state. The matrix looks the same regardless of whether the MSB or LSB is the control qubit.\n", + "\n", "$$\n", + "C_{u1}(\\lambda) = \n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 0 & 0 & e^{i\\lambda}\n", + "\\end{pmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.cu1(pi/2,q[0], q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I THINK SHOULD BE CALLED $C_\\mathrm{PHASE}(\\lambda)$" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j]])" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Controlled $u3$ rotation\n", "\n", - "However, when the LSB is the control qubit, (e.g. `cx(q[0],q[1])`), this gate is equivalent to the following matrix:\n", + "Perform controlled-$u3$ rotation on the target qubit if the control qubit (here LSB) is $|1\\rangle$. \n", "\n", "$$\n", - "C_X = \n", + "C_{u3}(\\theta, \\phi, \\lambda) \\equiv \n", "\\begin{pmatrix}\n", "1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", + "0 & e^{-i(\\phi+\\lambda)/2}\\cos(\\theta/2) & 0 & -e^{-i(\\phi-\\lambda)/2}\\sin(\\theta/2)\\\\\n", "0 & 0 & 1 & 0\\\\\n", - "0 & 1 & 0 & 0\n", - "\\end{pmatrix}. \n", - "$$\n", - "\n", - "#### Controlled $Y$ gate\n", - "\n", - "Apply the $Y$ gate to the target qubit if the control qubit is $|1\\rangle$, for when the MSB is the control\n", - "\n", - "$$\n", - "C_Y = \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & -i\\\\\n", - "0 & 0 & i & 0\n", - "\\end{pmatrix},\n", - "$$\n", + "0 & e^{i(\\phi-\\lambda)/2}\\sin(\\theta/2) & 0 & e^{i(\\phi+\\lambda)/2}\\cos(\\theta/2)\n", + "\\end{pmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.cu3(pi/2, pi/2, pi/2, q[0], q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ],\n", + " [ 0. +0.j , 0. -0.707j, 0. +0.j , -0.707+0.j ],\n", + " [ 0. +0.j , 0. +0.j , 1. +0.j , 0. +0.j ],\n", + " [ 0. +0.j , 0.707+0.j , 0. +0.j , 0. +0.707j]])" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NOTE I NEED TO FIX THIS AND DECIDE ON CONVENTION - I ACTUALLY THINK WE WANT A FOUR PARAMETER GATE AND JUST CALL IT CU AND TO REMOVE THIS GATE." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Swap gate\n", "\n", - "or when the LSB is the control\n", + "The swap gate exchange the first and second qubits. \n", "\n", "$$\n", - "C_Y = \n", + "{SWAP} = \n", "\\begin{pmatrix}\n", "1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & -i\\\\\n", "0 & 0 & 1 & 0\\\\\n", - "0 & i & 0 & 0\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & 1\n", "\\end{pmatrix}.\n", - "$$\n", - "\n", - "#### Controlled $Z$ (or, controlled Phase) gate\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.swap(q[0], q[1])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n", + " [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n", + " [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Toffoli gate ($ccx$ gate)\n", "\n", - "Similarly, the controlled Z gate flips the phase of the target qubit if the control qubit is $1$. The matrix looks the same regardless of whether the MSB or LSB is the control qubit:\n", + "The Toffoli gate flips the third qubit if the first two qubits (LSB) are both $|1\\rangle$.\n", "\n", "$$\n", - "C_Z = \n", + "C_{CX} = \n", "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 0 & 0 & -1\n", + "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", + "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n", + "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\n", "\\end{pmatrix}\n", - "$$\n", - "\n", - "### Controlled Hadamard gate\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [], + "source": [ + "q = QuantumRegister(\"q\", 3)\n", + "c = ClassicalRegister(\"c\", 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.ccx(q[0], q[1], q[2])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.-0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n", + " 0.+0.j],\n", + " [ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n", + " 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n", + " 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n", + " 1.-0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.-0.j, 0.+0.j, 0.+0.j,\n", + " 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.-0.j, 0.+0.j,\n", + " 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.-0.j,\n", + " 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 1.-0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n", + " -0.+0.j]])" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.round(result.get_data('test')['unitary'], 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Controlled swap gate (Fredkin Gate)\n", "\n", - "Apply $H$ gate to the target qubit if the control qubit is $|1\\rangle$. Below is the case where the control is the MSB qubit.\n", + "The controlled swap gate exchange the second and third qubits if the first qubit (LSB) is $|1\\rangle$.\n", "\n", "$$\n", - "C_H = \n", + "C_{SWAP} = \n", "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & \\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\\\\n", - "0 & 0 & \\frac{1}{\\sqrt{2}} & -\\frac{1}{\\sqrt{2}}\n", + "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\n", "\\end{pmatrix}\n", "$$" ] }, { "cell_type": "code", - "execution_count": 106, + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.cswap(q[0], q[1], q[2])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1., 0., 0., 0., 0., 0., 0., 0.],\n", + " [ 0., 1., 0., 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 1., 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., 0., 0., 1., 0., 0.],\n", + " [ 0., 0., 0., 0., 1., 0., 0., 0.],\n", + " [ 0., 0., 0., 1., 0., -0., 0., 0.],\n", + " [ 0., 0., 0., 0., 0., 0., 1., 0.],\n", + " [ 0., 0., 0., 0., 0., 0., 0., 1.]])" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "np.real(np.round(result.get_data('test')['unitary'], 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Non unitary operations\n", + "\n", + "Now we have gone through all the unitary operations in quantum circuits we also have access to non-unitary operations. These include measurements, reset of qubits, and classical conditional operations." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [], + "source": [ + "q = QuantumRegister(\"q\", 1)\n", + "c = ClassicalRegister(\"c\", 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Measurements\n", + "\n", + "We dont have access to all the information when we make a measurement in a quantum computer. The quantum state is projected onto the standard basis. Below are two examples showing a circuit that is prepared in a basis state and the quantum computer prepared in a superpostion state." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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pqViSZDqdXlRUdOvWLbEQiL6+PpvNHh0dlUy2jIMJy7U+iEgkOjg4+Pn5ubq6SmbQljcTNw5WYLO+0N/fX01NLT8/f3p6WlQIZ8rbs2cPJi7hSAeric+JEycAAAEBAV1dXVwu9+eff4YgyNLSUiynOw62YKYPPp8fGxu78HHL2tpacq8kHGxZrvmpjLS1tSFn4sbBlv8B5xKQuW30tQsAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.measure(q, c)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "{'0': 1000}" ] }, - "execution_count": 106, + "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "demoCircuit.cx(qr[0], qr[1]) # applying cnot gate\n", - "demoCircuit.cy(qr[0], qr[1]) # controlled-y\n", - "demoCircuit.cz(qr[0], qr[1]) # controlled-z\n", - "demoCircuit.ch(qr[0], qr[1]) # controlled-h" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n", + "result.get_counts('test')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Controlled rotation gates\n", - "\n", - "#### Controlled rotation around Z-axis\n", - "\n", - "Perform rotation around Z-axis on the target qubit if the control qubit (here MSB) is $|1\\rangle$.\n", - "\n", - "$$\n", - "C_{Rz}(\\lambda) = \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & e^{-i\\lambda/2} & 0\\\\\n", - "0 & 0 & 0 & e^{i\\lambda/2}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "#### Controlled phase rotation\n", - "\n", - "Perform $u1$ on the target qubit if the control qubit (here MSB) is $|1\\rangle$.\n", - "\n", - "$$\n", - "C_{u1}(\\lambda) = \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 0 & 0 & e^{i\\lambda}\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "#### Controlled $U$ rotation\n", - "\n", - "Perform controlled-$U$ rotation on the target qubit if the control qubit (here MSB) is $|1\\rangle$. \n", - "\n", - "$$\n", - "C_{u3}(\\theta, \\phi, \\lambda) \\equiv \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & e^{-i(\\phi+\\lambda)/2}\\cos(\\theta/2) & -e^{-i(\\phi-\\lambda)/2}\\sin(\\theta/2)\\\\\n", - "0 & 0 & e^{i(\\phi-\\lambda)/2}\\sin(\\theta/2) & e^{i(\\phi+\\lambda)/2}\\cos(\\theta/2)\n", - "\\end{pmatrix}.\n", - "$$\n", - "\n", - "They can be added to the circuit as below." + " The simulator predicts that 100 percent of the time the classical registor returns 0. " + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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EC6jZvwcHB6Fz02i05ORkmZPZTp8+nZiYuGzZsuEfDgwMiEQifcrwS6I7qLn/feLECdhy37x5c+Sxg8bGxt9995304Ct8ybxJSNCjzva7rq4uLi4OALB582Z4xpUCcCfzJiHBAO4syyORbtR9+vSpYksVk3mTaJSlS5f6+fnB6z179ri6uhIqRyXU1j+RSCTZ2dkAAHd3d6V5OWAy771798ok8x4aGoqNjVWXJBIStfVPXrx4AZNOocnWpUoy79E4duwYLFb7vHnzZtq0aXJzVIxFqqqqqqqqZs6ciSDIx48fRSLR4sWLiZWEIMibN2/odLrSzKPDMTAwUJt/NzY2wgsWi6XUWEEy76KiotbWVqyZ1eG979+/x3qXumAymerdZE4gTU1NZmZmjo6OEomkoaEBALBo0SJiJcHOxrx58zA1Iur0b+k53zDJr2IUJPMuKiqqqanB4d+BgYFjIlWV7vPixQuZ/fNjd2pLbf4tPcz75cuXSo1xJ/Mm0QKBgYHStKZfffWVm5sboXJUQm3+PXv27OnTp7e0tOTk5FRWVs6bN0/G4Pnz54WFhTBNKL5k3or57bffiDqJqry83MHBwcLCgpDaNcTly5clEsns2bMBAH///TexYhAE4XK5LBYL06lAhmpMf0OlUmNiYoKDgwcHB9euXRsfH7969WozM7Pm5ubi4uKsrKx79+7t378fGtNoNJFINLIQxcm8FdPe3v727VtVHgE3HR0dBgYG2jmQSWu8f/9eIpEMDQ0RLQQAABAE+fDhA4/Hw5S01sTERJ3z3xKJ5MsvvxytMktLy+zsbGjp6OgIABgYGJApISgoCABQVFSkRlUk4xl1xucpFEpOTs7JkydljnucO3duXFxcQ0ODNLmeNJm3TAkKknmTkOBAI+cPisViOB1uaWnJYDBGZijetWvXrVu38vLyZKbAbW1tBQJBR0eH3swlkxCLRvY3GBkZeXh4eHt7e3l5yU2/jSOZNwkJDojZn4Y1mTcJCU6I6vgfP34cALBp06ba2lqRSHTx4kUKhcJisfr6+oiSRKJ/EHb+99DQUGRkZFJSklQATOZtb29PiB4SvYTg8+1fvXqlNJk3CQlu/g/izLp9pLKdKgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.h(q)\n", + "qc.measure(q, c)\n", + "circuit_drawer(qc)" ] }, { "cell_type": "code", - "execution_count": 107, + "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "{'0': 474, '1': 526}" ] }, - "execution_count": 107, + "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "demoCircuit.crz(lambd, qr[0], qr[1]) # controlled rotation around-Z\n", - "demoCircuit.cu1(lambd, qr[0], qr[1]) # controlled u1\n", - "demoCircuit.cu3(theta, phi, lambd, qr[0], qr[1]) # controlled u3" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n", + "result.get_counts('test')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Swap gate\n", - "\n", - "The swap gate exchange the first and second qubits. \n", - "\n", - "$$\n", - "{SWAP} = \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1\n", - "\\end{pmatrix}.\n", - "$$" + " The simulator predicts that 50 percent of the time the classical registor returns 0 or 1. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Reset\n", + "It is also possible to `reset` qubits to the $|0\\rangle$ state in the middle of computation. Note that `reset` is not a Gate operation, since it is irreversible." ] }, { "cell_type": "code", - "execution_count": 108, + "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 108, + "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "demoCircuit.swap(qr[0], qr[1]) # swapping the first and second qubits" + "qc = QuantumCircuit(q, c)\n", + "qc.reset(q[0])\n", + "qc.measure(q, c)\n", + "# circuit_drawer(qc)" ] }, { - "cell_type": "markdown", + "cell_type": "code", + "execution_count": 65, "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'0': 1000}" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "### Toffoli gate ($C3$ gate)\n", - "\n", - "The Toffoli gate flips the third qubit if the first two qubits (MSB) are both $|1\\rangle$.\n", - "\n", - "$$\n", - "C_{CX} = \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", - "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "### Controlled swap gate (Fredkin Gate)\n", - "\n", - "The controlled swap gate exchange the second and third qubits if the first qubit (MSB) is $|1\\rangle$.\n", - "\n", - "$$\n", - "C_{SWAP} = \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n", - "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\n", - "\\end{pmatrix}\n", - "$$" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n", + "result.get_counts('test')" ] }, { "cell_type": "code", - "execution_count": 109, + "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 109, + "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "demoCircuit.ccx(qr[0], qr[1], qr[2]) # Toffoli gate\n", - "demoCircuit.cswap(qr[0], qr[1], qr[2]) # swapping the second and third qubits controlled by the first qubit" + "qc = QuantumCircuit(q, c)\n", + "qc.h(q)\n", + "qc.reset(q[0])\n", + "qc.measure(q, c)\n", + "#circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'0': 1000}" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n", + "result.get_counts('test')" ] }, { "cell_type": "markdown", - "metadata": { - "collapsed": true - }, + "metadata": {}, "source": [ - "## Remark on the equivalence of gates up to the global phase \n", - "\n", - "In the above we see that the one-qubit $X$ gate is equivalent to the $u3(\\pi, 0, \\pi)$ gate up to the global phase, but the global phase can be tricky with controlled gates. For example, the $C_X$ gate (or, the control NOT gate) is not equivalent to the $C_{u3}(\\pi, 0, \\pi)$ gate. This is because:\n", - "\n", - "$$\n", - "C_{u3}(\\pi, 0, \\pi) \\equiv \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & -j\\\\\n", - "0 & 0 & -j & 0\n", - "\\end{pmatrix} \\neq \n", - "\\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", - "0 & 0 & 1 & 0\n", - "\\end{pmatrix} = C_X\n", - "$$ " + "Here we see that for both of these circuits the simulator always predicts that the output is 100 percent in the 0 state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## State Initialization\n", - "\n", - "When a qubit register is declared, the qubits start out initialized to the $|0\\rangle$ or ground state. This is convenient in superconducting qubit technology, as well as many other technologies." + "### Conditional operations\n", + "It is also possible to do operations conditioned on the state of the classical registor" ] }, { "cell_type": "code", - "execution_count": 110, + "execution_count": 68, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, + "execution_count": 68, "metadata": {}, - "output_type": "display_data" + "output_type": "execute_result" } ], "source": [ - "# A declared register starts out at the |00..0> state\n", - "initialize_circuit = Q_program.create_circuit('initialize_circuit', [qr], [cr])\n", - "initialize_circuit.measure(qr, cr)\n", - "circuits = ['initialize_circuit']\n", - "result = Q_program.execute(circuits, backend='local_qasm_simulator', shots=1024)\n", - "plot_histogram(result.get_counts('initialize_circuit'))" + "qc = QuantumCircuit(q, c)\n", + "qc.x(q[0]).c_if(c, 0)\n", + "qc.measure(q,c)\n", + "# circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'1': 1000}" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n", + "result.get_counts('test')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Reset\n", - "It is also possible to `reset` qubits to the $|0\\rangle$ state in the middle of computation. Note that `reset` is not a Gate operation, since it is irreversible." + "Here the classical bit always takes the value 0 so the qubit state is always flipped. " ] }, { "cell_type": "code", - "execution_count": 111, + "execution_count": 70, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "" + "" ] }, + "execution_count": 70, "metadata": {}, - "output_type": "display_data" + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(q, c)\n", + "qc.h(q)\n", + "qc.measure(q,c)\n", + "qc.x(q[0]).c_if(c, 0)\n", + "qc.measure(q,c)\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'1': 1000}" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "# A reset statement takes qubits back to |0>\n", - "reset_circuit = Q_program.create_circuit('reset_circuit', [qr], [cr])\n", - "reset_circuit.x(qr)\n", - "reset_circuit.h(qr)\n", - "reset_circuit.reset(qr)\n", - "reset_circuit.measure(qr, cr)\n", - "circuits = ['reset_circuit']\n", - "result = Q_program.execute(circuits, backend='local_qasm_simulator', shots=1024)\n", - "plot_histogram(result.get_counts('reset_circuit'))" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n", + "result.get_counts('test')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the classical bit by the first measurement is random but the conditional operation results in the qubit being deterministically put into $|1\\rangle$." ] }, { @@ -963,18 +2431,19 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": 72, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Desired probabilities...\n", - "['0.062', '0.125', '0.125', '0.000', '0.000', '0.625', '0.062', '0.000']\n", - "Probabilities from simulator...\n", - "['0.062', '0.138', '0.116', '0.000', '0.000', '0.625', '0.059', '0.000']\n" - ] + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ @@ -989,21 +2458,74 @@ " 1 / math.sqrt(8) * complex(1, 2),\n", " 1 / math.sqrt(16) * complex(1, 0),\n", " 0]\n", - "initialize_circuit_3q = Q_program.create_circuit('initialize_circuit_3q', [qr], [cr])\n", - "initialize_circuit_3q.initialize(\"init\", desired_vector, [qr[0],qr[1],qr[2]])\n", - "initialize_circuit_3q.measure(qr, cr)\n", - "circuits = ['initialize_circuit_3q']\n", - "result = Q_program.execute(circuits, backend='local_qasm_simulator', shots=1024)\n", "\n", - "print(\"Desired probabilities...\")\n", - "print(str(list(map(lambda x: format(abs(x * x), '.3f'), desired_vector))))\n", "\n", - "print(\"Probabilities from simulator...\")\n", - "counts = result.get_counts(\"initialize_circuit_3q\")\n", - "qubit_strings = [format(i, '0%sb' % n_qubits) for\n", - " i in range(2 ** n_qubits)]\n", - "print([format(counts.get(s, 0) / 1024, '.3f') for\n", - " s in qubit_strings])" + "q = QuantumRegister(\"q\", 3)\n", + "c = ClassicalRegister(\"c\", 1)\n", + "\n", + "qc = QuantumCircuit(q, c)\n", + "\n", + "qc.initialize(desired_vector, [q[0],q[1],q[2]])\n", + "circuit_drawer(qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2.50000000e-01+0.00000000e+00j, 5.55111512e-17-3.53553391e-01j,\n", + " 2.50000000e-01-2.50000000e-01j, -2.19980517e-18-3.09536077e-17j,\n", + " -2.62603921e-17+5.08377096e-17j, 7.07106781e-01-3.53553391e-01j,\n", + " 8.67361738e-17-2.50000000e-01j, 0.00000000e+00+0.00000000e+00j])" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qp = QuantumProgram()\n", + "qp.add_circuit(\"test\", qc)\n", + "result = qp.execute(['test'], backend='local_unitary_simulator')\n", + "ground = np.zeros(2**3)\n", + "ground[0]=1.0\n", + "qc_state = np.dot(result.get_data('test')['unitary'], ground)\n", + "qc_state" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [], + "source": [ + "def norm(state1, state2):\n", + " return abs(np.dot(np.array(state1).conj(), state2))**2" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "norm(desired_vector,qc_state)" ] }, { @@ -1046,17 +2568,17 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Version information

\n", - "

Please note that this tutorial is targeted to the stable version of the QISKit SDK. The following versions of the packages are recommended:

\n", + "

Please note that this tutorial is targeted to the stable version of the QISKit. The following versions of the packages are recommended:

\n", "\n", "\n", - "\n", + "\n", "\n", "\n", "\n", @@ -1072,8 +2594,15 @@ } ], "source": [ - "%run \"../version.ipynb\"" + "%run \"../../version.ipynb\"" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -1093,7 +2622,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.4" } }, "nbformat": 4, diff --git a/reference/tools/visualizing_quantum_state.ipynb b/reference/tools/visualizing_quantum_state.ipynb index 222fc7518..4483e3544 100644 --- a/reference/tools/visualizing_quantum_state.ipynb +++ b/reference/tools/visualizing_quantum_state.ipynb @@ -4,14 +4,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\"Note: Trusted Notebook\" width=\"250 px\" align=\"left\">" + "\"Note: Trusted Notebook\" width=\"250 px\" align=\"left\">" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## _*Visualizing a Quantum State*_ \n", + "## _*Visualizing a Quantum Data and States*_ \n", "\n", "The latest version of this notebook is available on https://github.com/QISKit/qiskit-tutorial.\n", "\n", @@ -23,39 +23,74 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# Checking the version of PYTHON; we only support >= 3.5\n", + "# Checking the version of PYTHON; we only support > 3.5\n", "import sys\n", "if sys.version_info < (3,5):\n", " raise Exception('Please use Python version 3.5 or greater.')\n", " \n", + "try:\n", + " sys.path.append(\"../../\") # go to parent dir\n", + " import Qconfig\n", + " qx_config = {\n", + " \"APItoken\": Qconfig.APItoken,\n", + " \"url\": Qconfig.config['url']}\n", + "except:\n", + " qx_config = {\n", + " \"APItoken\":\"YOUR_TOKEN_HERE\",\n", + " \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ "# useful additional packages \n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", - "from scipy import linalg as la\n", - "\n", - "# importing the QISKit\n", - "from qiskit import QuantumCircuit, QuantumProgram\n", - "import Qconfig" + "from pprint import pprint\n", + "from scipy import linalg as la" ] }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 3, + "metadata": {}, "outputs": [], "source": [ + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n", + "from qiskit import QuantumProgram\n", + "\n", "# import state tomography functions\n", "from qiskit.tools.visualization import plot_histogram, plot_state" ] }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def ghz_state(q, c, n):\n", + " # Create a GHZ state\n", + " qc = QuantumCircuit(q, c)\n", + " qc.h(q[0])\n", + " for i in range(n-1):\n", + " qc.cx(q[i], q[i+1])\n", + " return qc\n", + "\n", + "def superposition_state(q, c):\n", + " # Create a Superposition state\n", + " qc = QuantumCircuit(q, c)\n", + " qc.h(q)\n", + " return qc" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -70,59 +105,51 @@ "plot_histogram(result.get_counts('circuit'), number)\n", "```\n", "\n", - "The generated bar graph is simple to understand. The height of each bar represents the fraction of instances the corresponding outcome is obtained within the total number of runs on the backend. Only those outcomes that occurred at least once are displayed. The optional parameter `number` specifies the total number of bars to be displayed. All remaining probability is collected into a single bar labeled \"rest\". Quantum circuits for most quantum algorithm will typically have one outcome (representing the desired solution to the problem), or at most a few outcomes. Only circuits that produce superpositions of many computational states as their final state will give many outcomes, and collecting those could require an exponentially large number of measurements. To demonstrate this, we study two circuits: a GHZ state and a superposition state involving 3 qubits. " + "The generated bar graph is simple to understand. The height of each bar represents the fraction of instances the corresponding outcome is obtained within the total number of shots on the backend. Only those outcomes that occurred at least once are displayed. The optional parameter `number` specifies the total number of bars to be displayed. All remaining probability is collected into a single bar labeled \"rest\". Quantum circuits for most quantum algorithm will typically have one outcome (representing the desired solution to the problem), or at most a few outcomes. Only circuits that produce superpositions of many computational states as their final state will give many outcomes, and collecting those could require an exponentially large number of measurements. To demonstrate this, we study two circuits: a GHZ state and a superposition state involving 3 qubits. " ] }, { "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, + "execution_count": 5, + "metadata": {}, "outputs": [], "source": [ "# Build the quantum cirucit. We are going to build two circuits a GHZ over 3 qubits and a\n", "# superpositon over all 3 qubits \n", - "Q_program = QuantumProgram()\n", + "\n", "n = 3 # number of qubits \n", - "q = Q_program.create_quantum_register('q', n)\n", - "c = Q_program.create_classical_register('c', n)\n", + "q = QuantumRegister(\"q\", n)\n", + "c = ClassicalRegister(\"c\", n)\n", "\n", "# quantum circuit to make a GHZ state \n", - "ghz = Q_program.create_circuit('ghz', [q], [c])\n", - "ghz.h(q[0])\n", - "ghz.cx(q[0], q[1])\n", - "ghz.cx(q[0], q[2])\n", - "ghz.s(q[0])\n", - "ghz.measure(q[0], c[0])\n", - "ghz.measure(q[1], c[1])\n", - "ghz.measure(q[2], c[2])\n", + "ghz = ghz_state(q, c, n)\n", + "\n", "\n", "# quantum circuit to make a superposition state \n", - "superposition = Q_program.create_circuit('superposition', [q], [c])\n", - "superposition.h(q)\n", - "superposition.s(q[0])\n", - "superposition.measure(q[0], c[0])\n", - "superposition.measure(q[1], c[1])\n", - "superposition.measure(q[2], c[2])\n", + "superposition = superposition_state(q, c)\n", "\n", - "circuits = ['ghz', 'superposition']\n", + "measure_circuit = QuantumCircuit(q,c)\n", + "measure_circuit.measure(q, c)\n", "\n", "# execute the quantum circuit \n", "backend = 'local_qasm_simulator' # the device to run on\n", - "result = Q_program.execute(circuits, backend=backend, shots=1000)" + "qp = QuantumProgram()\n", + "qp.add_circuit(\"ghz\", ghz+measure_circuit)\n", + "qp.add_circuit(\"superposition\", superposition+measure_circuit)\n", + "circuits = ['ghz', 'superposition']\n", + "result = qp.execute(circuits, backend=backend, shots=1000)" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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bAHe5+62VtrcCFhPmv9oFTHD3LdG2/sCdwMnAYWBItGKgiIjELJXE8UVgM/DP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\n/6amVYhSdJgjAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -150,8 +177,38 @@ "source": [ "### Method for visualizing a quantum state\n", "\n", - "For educational and debugging purposes, it is useful to visualize the quantum state given by a density matrix $\\rho$. Experimental reconstruction of a quantum state requires $4^n-1$ different measurements, where $n$ is the number of qubits. Results from these measurements are then combined using a process known as [quantum state tomography](../3_qcvv/state_tomography.ipynb) to estimate the quantum state.\n", + "For educational and debugging purposes, it is useful to visualize the quantum state given by a density matrix $\\rho$. This can not be obtained from a single shot of an experiment or simulation of quantum cirucit. However, in QISKit we have also provided a unitary simulator, which provided you dont place measurements these backends will return the quantum state.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "n = 2 # number of qubits \n", + "q = QuantumRegister(\"q\", n)\n", + "c = ClassicalRegister(\"c\", n)\n", + "\n", + "qc = QuantumCircuit(q, c)\n", + "qc.h(q[1])\n", "\n", + "\n", + "# execute the quantum circuit \n", + "qp = QuantumProgram()\n", + "qp.add_circuit(\"superposition\", qc)\n", + "circuits = ['superposition']\n", + "backend = 'local_unitary_simulator' # the device to run on\n", + "result = qp.execute(circuits, backend=backend, shots=1000)\n", + "ground = np.zeros(2**n)\n", + "ground[0]=1.0\n", + "state_superposition = np.dot(result.get_data('superposition')['unitary'], ground)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "#### Pure states\n", "\n", "A pure state $\\left|\\psi\\right\\rangle$ is an element of the Hilbert space $\\mathcal{H}$. For $n$ qubits, the Hilbert space is the complex vector space $\\mathbb{C}^{d}$ with dimension $d=2^n$. We denote the inner product between quantum states by $\\left\\langle \\phi \\right| \\psi \\rangle$. We denote the canonical set of orthonormal basis vectors spanning $\\mathcal{H}$ as $\\left| i\\right\\rangle$ where $i\\in {0,...,d-1}$ and $\\left\\langle j \\right| i \\rangle =\\delta_{i,j}$. This allows us to define an arbitrary pure state, state vector, or ket as\n", @@ -166,8 +223,52 @@ "\n", "$$\\left\\langle \\phi \\right| \\psi \\rangle = \\sum_{i=0}^{d-1} \\phi^*_i \\psi_i.$$\n", "\n", - "We require the state vector to be normalized, $\\left\\langle \\psi \\right| \\psi \\rangle = \\sum_{i=0}^{d-1} |\\psi_i|^2 =1$. As a result, $(d - 1)$ complex numbers are necessary to describe an arbitrary pure state.\n", + "We require the state vector to be normalized, $\\left\\langle \\psi \\right| \\psi \\rangle = \\sum_{i=0}^{d-1} |\\psi_i|^2 =1$. As a result, $(d - 1)$ complex numbers are necessary to describe an arbitrary pure state.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def overlap(state1, state2):\n", + " return round(np.dot(state1.conj(), state2))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.70710678+0.j 0. +0.j 0.70710678+0.j 0. +0.j]\n" + ] + }, + { + "data": { + "text/plain": [ + "(1+0j)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(state_superposition)\n", "\n", + "overlap(state_superposition, state_superposition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "#### Operators\n", "\n", "In order to relate the state to quantities of physical interest, we need to introduce operators. An operator is an object which maps a state from Hilbert space onto another state. Hence, in Dirac notation an operator can be written as\n", @@ -177,7 +278,54 @@ "where $a_{ij}$ are complex numbers. For a given state $\\left|\\psi \\right\\rangle$, the mean or expectation value of $A$ is written as \n", "\n", "$$\\langle A \\rangle = \\left\\langle \\psi \\right|A \\left|\\psi\\right\\rangle. $$ \n", - "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def expectation_value(state, Operator):\n", + " return round(np.dot(state.conj(), np.dot(Operator, state)).real)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Operator Z on qubit 0 is 1.0\n", + "Operator Z on qubit 1 is 0.0\n", + "Operator X on qubit 0 is 0.0\n", + "Operator X on qubit 1 is 1.0\n" + ] + } + ], + "source": [ + "X = np.array([[0, 1], [1, 0]])\n", + "Z = np.array([[1, 0], [0, -1]])\n", + "IZ = np.kron(np.eye(2), Z)\n", + "ZI = np.kron(Z, np.eye(2))\n", + "IX = np.kron(np.eye(2), X)\n", + "XI = np.kron(X, np.eye(2))\n", + "\n", + "\n", + "print(\"Operator Z on qubit 0 is \" + str(expectation_value(state_superposition, IZ)))\n", + "print(\"Operator Z on qubit 1 is \" + str(expectation_value(state_superposition, ZI)))\n", + "print(\"Operator X on qubit 0 is \" + str(expectation_value(state_superposition, IX)))\n", + "print(\"Operator X on qubit 1 is \" + str(expectation_value(state_superposition, XI)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "\n", "#### Mixed states\n", "\n", @@ -200,7 +348,7 @@ "```\n", "This draws two 2-dimensional bargraphs (for the real and the imaginary part of $\\rho$). Note that the diagonal is necessarily real and sums to 1 (due to normalization), and $\\rho_{i,j} =\\rho_{j,i}^*$ due to Hermiticity.\n", "\n", - "It can be useful to interpret operators as vectors in a complex space of dimensions $d^2$ ($\\mathbb{C}^{d^2}$). To access the element $a_{ij}$, we use $a_p$ where $p = i + jd$. The indices $i$ and $j$ associated with a given $p$ are given by $i = p \\% d$ and $j = \\mathrm{floor}(p/d)$. We will use double-ket notation $\\mid A \\rrangle$ to represent the matrix $A$ as a vector in the operator vector space. In this operator space, we also define an inner product in the standard way:\n", + "It can be useful to interpret operators as vectors in a complex space of dimensions $d^2$ ($\\mathbb{C}^{d^2}$). To access the element $a_{ij}$, we use $a_p$ where $p = i + jd$. The indices $i$ and $j$ associated with a given $p$ are given by $i = p \\% d$ and $j = \\mathrm{floor}(p/d)$. We will use double-ket notation $\\mid A \\rangle$ to represent the matrix $A$ as a vector in the operator vector space. In this operator space, we also define an inner product in the standard way:\n", "\n", "$$\n", "\\newcommand{\\llangle}{\\langle\\!\\langle}\n", @@ -238,103 +386,45 @@ }, { "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# execute the quantum circuit \n", - "backend = 'local_unitary_simulator' # the device to run on\n", - "result = Q_program.execute(circuits, backend=backend, shots=1000)\n", - "\n", - "ground = np.zeros(2**n)\n", - "ground[0]=1.0\n", - "\n", - "state_superposition = np.dot(result.get_data('superposition')['unitary'],ground)\n", - "rho_superposition=np.outer(state_superposition, state_superposition.conj())\n", - "\n", - "state_ghz = np.dot(result.get_data('ghz')['unitary'],ground)\n", - "rho_ghz=np.outer(state_ghz, state_ghz.conj())" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Y8YsddPR2sLFlIzsO7+CTnZ9g99sxDZgYdAyGIj8RlVLFmQ1ncseX7uCsxrPw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\nMDExwdixY3Hjxg2MHz8eQ4YMwdWrVxEYGKj3sfnlPWx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4ssUUfIR3Gt7hu+DLb3fgyvkN3PgchSuoCyIfW+Gd+VoqyuxkfMnl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\nKMX/B4aQCKR1JbeaAAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "plot_state(rho_ghz,'paulivec')" + "def state_2_rho(state):\n", + " return np.outer(state, state.conj())" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The 0th eigenvalue = 1.0\n" + "[[0.5+0.j 0. +0.j 0.5+0.j 0. +0.j]\n", + " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]\n", + " [0.5+0.j 0. +0.j 0.5+0.j 0. +0.j]\n", + " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]]\n" ] - }, - { - "data": { - "image/png": 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zacjIGGhIFTdv3gQA1NbWwu/361qWyIqalTY/A7nifU75FHKMdFVheNJKomQY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\nIL3/A3o9467DBRQjAAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ - "plot_state(rho_ghz,'qsphere')" + "rho_superposition=state_2_rho(state_superposition)\n", + "print(rho_superposition)" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { - "image/png": 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T6XXNhJiG2huOjY1RUlJCfX192ISaaI9NZK34ze9LC3Z9w33sOLqDt3rf4tU3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\nVSkC9DdRENZg6iN+mQJb6eUSEW7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XuaysDEVFRSgrK+M6+nh5eZncqaguaDQanD17FqtW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\nMBXAswDetHubdjQEdmNqx2MFgYHpCmAztAampznGhWGYIQAmATg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+ "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -347,14 +437,14 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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QT7p69N8dNlzRTcKnitvmwnfFO9aNUZnP4aO2h3BF9A18ZPwjfFR4N650f44r\n1H8Da2UjgTjnstgfgCvMN3GDMgpvoBPw5ZRz8c62JBrEcfgS2ki8ob8S562AN/o7Q4ZZuJHZF+/4\nx+AjmA3wDrkibhSmAOvm8toPVz5X4qP5z+Ad7dRUG42vHWmeHmHL4QZwPr5E9mN8lPoEtbXkD+J+\npPfwUehX8A72x7jeNHzU92r8/xqu1EZHOc+KcpuGK663cCN7OK5E38VHxXfhnXoublRexY3yRHyG\n8l7I9jaujObho8k3qM0IZ+AGcEqkm6LsDoj6mBJ5XRD18lxc43Z8FLkEN7Cn4orsuUjjRlyhHRZy\n/TPKe/lcHWdO6hmR1mhcWayGj0yfxmcFd+dGzjND7mxZ8zrcSPwpyvHaqMMF+Gj5fnx5ad3Yn4+3\nt+vx2cvcKO+Tc/HuxGc3d0Y+luCDgTm4IT0FnwW+E+VzPT7DnRsy/AXvIztEvl6Kerot5Hw9zjsU\nV+T98VH9pCi/1/H2NDvy8QruizoNHyRMj/9eibJdFPGy5eU7oy7fC5myZeXX8DZ1Nd6vrsNXHl6I\ndN7A++Zz+Cxt26jr+/B+Nh43zAuBS6L8V4rz5gB3RdjPomzuiOsYboQStVnCz+Kcd6n5VY6IunkN\nuDnCjon6voNw+OOGM1GbmR8T590DHJyTaz45P2vddGdXK+/usOEjvp/hI8y7cQV2ajTC7C6hXaIS\n/oWPTp6O/xfhI4ed8JHkMXH+PbgyuAsYFGlsEsdfwI3TbHyUPCH+3yga8A244/FruFJ+DVdSM3AD\nlXXkx/Dlpr1xY/ISPp1/HFcQP450x8R5v8VHeCuGzM/F+ctHvI/iCuAsXMFtghuUT1Fb1tk0ZBmO\nO+xvwWdWz+GKfXd8dvIwvtRwHK7sx+OjrlejLG/EZ1lb4Mbp/MjPkXFeL3zmNQ83rjviI93vRD5f\nwJXBFXhHn4crv3Mi/n9w43F//N4b8a6Pa/YCtow89cLbwFH47GUEbpQ3xEfTf4synYTPusbhg4PZ\nkZ8lEX4V3iYy43MXPhL8Ha4034rrP0L4avA29XaU/Y5x/oaRx6kR58Uo1/fw2S+5c98jPouAL/0t\nxgcwg6Nc/xPnDsUVdbZm/tu4VnbuQHzQMQXYJcI+FuX8Gt4f1ohyuom4+yzi7RHXnBL56B319H5a\nEe9SfJaQ3YG2ZsR7hJqfY228rXwNX75ZH1/i2jT2v4H3rSfw9rEjPog6J8p556i/m/FVhIm4A/t0\n3KBujM9gbQpfAAAWKUlEQVRAP4e3tbtxI3s4PlgcHNc4IhfnFnwGdSo+EFsp4m6B97cZId+38L5x\nV4Qth+uKy/FZwrN42z4ZNzzP4P1sIm5kX8FnpBb52xtvZ1OibB7B+20+rYNwg5nFeTBk+zYwOcK+\nC9zeEN3Z1cq7q7do7AfgywObReX8Ah/tzojth1FZf4+G9dFolDPxUc2L+BLDxdScn9vha7pvRXob\n46P6O3BF9g7wh4j7JLWRfqbUslHDCHwkPjM6y+r41Pvr+DLMldEQl8dHyTeG7O/iCvHWaISL4zrj\ncWWaGcArcAVwHT4qzEZw5+Ejy8X4rOMP1EalD0RDfTbyNjDkeDdkXx7vdH+KTvEwbuCuwhXayIiX\n3X21U+QhWy/fItIwfGR8D668+uDG6dboTFvjyj8bje4Y5yyPd9qXcaX6SdwwfD/yvwGuHA6M/Wwp\nty9uNFei6e3MO+N3wmTryV8kRndxvD2upL8W5/fFBwPr4gppeXzZ6BB8DfyHuBL+Eq6gL8aX166h\ndivr41FPn8EN48CQ/Ul8VrIjbniujPrtE3meEGW4HD7qf5m4GQSf/c0OOXvhg5Nn8LZ/XJTR4Xi7\n2DJkzsfbBm9Tp+PtZ1N8CS27G+4Pce2DQsZ8Wqvjs4sszrr4TOOYCHsCNyjDaXp3Vm/cT5IZ3H4h\na3aHoUX80dQc5L2ivA4lbpTIhY8Cro/j/nibGJS7Xi/cKJwdxwNww7V6lLHl4m4f8U+Ocn+RuB2c\n2g0rC6jdZHAp3gdexg1GFucVvE38Be+DG+EDk8F4W7wBHyy9Su0W7iytGfiNL1mc2bn83ooPBp8C\n9pYBaYwByZxYj1Bzeg7F/QDfx5XkC9Qc3Y9GZR8WjWMLfP37AXwdNGuE2wG/xEc3S/Cp9mO4Ur0d\nV/D7R/xdcMWwda5xHhHxsk4yGjgjU3SFPKwajeg0fCT+Nj4CnkFt+v8QPqq9HF8SuR5fHlgSDXhm\n/D8r8ptN3+/GFdljkc5CfIQ1AR/9Xot36BvjnGxEuyduPP8GvBphr+LGejZLf0zsVtzHcyq+tLAJ\nrthWw5Xk3dQU4XKR7j240RmCd+LriedRqN0982fc0E7AO+i9+CzyVFxhXx3l8WXcoNyFL8t8DR9t\n/wD4ak7W3lEXf4n9XvH7U1wp9ImwFeK6Q3JG6LuRxxXxZawl+FLeZvgy3JJc/KH4YGMJNeW+Cz6b\n/Dm+jHIeXve34cpyLq4wpuEj+9F4G/hcpGn4wGca8J0IG4MvwZ4dddg7yuOykDG7ffUyvM3/DVd8\nZ0dZXhXxshtRbgqZswFRlta5wLkRdjM+MNofb2/b4wrxz5HnbIaSDcZ+gvePdeP47Eijd66urwcu\nKPSLK4CLc8fL4e03W3Ltgw+QRhbiLMb70J658BOp3c2W3dk1gZohmxD5PgUf5KyJL0tNjjLpFfX+\nJN43PxxxXo58Xx7ldEukMyrqeBzeDpfEeafm8jwlwv6E95clwF9zMn+YWCJtmP7sagXeXTZ8yeIQ\nfOT372gwO+FT2Dn4Estoauvo04Hn4ty1cQX8PdxwvBid653oGBfgnfP8OH4r0rgXHzkcjSu1V3Fn\n2pa44j8SH72fjE+r51Cb8v8GHxEuh98efFd0mHOiIT0YneUH+IxpDWpK/q7I667RQF/Hjden4tz9\nonHvjyvK+SH3z/HOOxxXwHdTu9X1TXzk9gI1JfhONOCbcEX/KK5UZ+DLIsdGGS8MOTJlfmekOwF3\nUn4LV7SHEc9v4J32dty4XILffXZPlMHReEfeEB8AXBp5PSmu8yZu/P6M+5RG4YbwYVwZ3hh5uxKf\ndT5O3ImHK9ihUYZfyLWfqZHutnH8BVwZnhf1eCE+0MjymN1Bc3/IdRyujAfEf/vgvqy3cUVwEd7+\ntsQN8BJ8yWZ5fAa5JPK/H95O5lBTaM8CG+Ta+fm48lkHN76DqT2fcQU+W/4u7sC/IM7bjJrSmxx5\nuJmcQo54I6Mcngi51sUNc+YD2xNfGssM0zFRvl+L+j0Wn6V+JsrlA1HX5+KDtDWo+euuwUfoh+BK\n9n2fXaS9Vsia+RqKS67HU/PZZQOfG/B29wV85L5OhO9HzdgdgRuDY6n5FzekduNNVrabxn+Zb7Ev\nPhB4OFeuO0TcrFwvwQcCW1LzL/4IHxhk5frVOPez+IpBVq5b5eTNlpz3Bg6RAelcY3JwNIK3otJe\njw5wOa5EX8RH+ldHI1kJX3N8IDrNbviyyVx85HFFVPL90YjPxA3AztEIr8NnCPNwpXMfPkM5NbYL\ncIU2oZmwf+JKap2c/EeGjCPj2tkzFkfiSixzgq+PK/N/RBoDI48/i//7RP6WkHtSG+/Q3wDWiONP\nRPn0j7T+NzrTFNygfB9XNkfhivxLuMF9EDcqS3AF8XtcmV9HTZnfjCvrTJk/hhvp7PmQvF/p4/hy\nSOY43gY36rOp+bLWxWdqb1Bbn/4rrsDfxY3X9ZGPY+P6c/HOfRQ1f9b3qN0yvFVc4zfU/Fm7UjNa\nN+DG9J/4iP/vkf5juEG7KfJwdVzzLLytDMYVS++ohyyf3478LQC2ieudSO3GhaOJpcM4HhX52BT3\n9a1GzQd2GjUf2PqR9zPwNrMeTW+kWC7KfXPceF9MU4U8FB/c5P1gJ+KDgfEh+wxi6TbXni7FB21H\nRVlkz05lSnYgrrj/jfeNPaL8Zkc9Zk7stnx2D1EbgFwc9bo7boAeDvneo/bE9z3AA7HfL8r1GeD5\nnOx/i7L9VcQZmC/biLMGXvf74IOhJsYuV66bhayHUc6/eD3eXrNy/X0zuuxIYGUZkM4zHr2ioR4d\nlb0rPjt4A1d6/8RH/PNwBTA5GvM28d8N+GjkTHxKmj2kdjC+dLA/7vzbFFe4A/GO94vobA/Glj13\n8Wikeyau5LKwzNl9Jm7oJuMd8Vv4qO06XJnehY/yhka8M0PuvSKvx0VDvRd3ou4YDXTHKI/zcENw\nG7XRzYbRqHeMxr8CtYerto5rzsdvEHgbV2Zv4SPb50KWXamt686hpswvxZf+2lLmR1O7cylT5rvh\niiZT5nfG/8eHfNny1mB8yWoK7kzOlqSmRzkcSSxHRvwv4oOIp0P2z+DLBlMif/+i5rt4Ep8FPkfN\naGW3C98dcvyT2t1Bd8ZxlsdxES+7AWMVasuaWT5/iCvZ92/ASDXDnvlpsudvjsaV9zv4bOEFyvnA\nfoU7dD8b6Xwq0l0Vb7MPRJ3+GVfcl+HGcR41/9XESCuvuGfjNyN8D2/vD4dMidoDp7uHbJfg7eJZ\narPGJVFmp+Mzlf/gBu9wancpNeezexTvw5uE/DtHWnuErLfgM6GF1AzqHXg73iZXxs/js4DDad2/\nOCvK9jtRtvMj3iMlyrWsf/G9Yrlmxi5+twemNVRfdrXC7u4b7jw7DLfyM3Fl1I/aazw+iyu+jaIx\nLo7KX4DPVraNhvkIrhCm4orqCVxx7YWPqLM4k6NhHxLxnsM74FTcf5APexJXbv+Hj8xGRoPeMOR6\nCF8bfxVftpiOj/BOwjt8L3z57RZcOb+GG5/DcAV1TuRjc7wzX0lNmR2PL7kcgE+xs+vtiDtHF+Mj\n36fxdd7xcd4JuBLtF+W2GF/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lID0cEWvk2wIeakw3PW4FcAOwAjgpIn7aS7zZwGyASZMmTZ07d+5A0lvF8uXLmThxYsfFqjteJ+dWd7xOzq3ueJ2cW93xnFt1M2bMuD4ipvX7wIho+wX4FXBjD5eZwMNNj32olxgb5OtNgb8Bm/X3ulOnTo26XXXVVR0Zq+54nZxb3fE6Obe643VybnXHc27VAQuixLa97PlABiQiduntPkn3SFovIu7OR/y9t5cYd+XrpZLmA9sCt7cjXzMz618rx8Jql3nAB/LtDwCXND9A0pqSxuTbawOvB24atAzNzGwVnVBATgJ2lXQbsEueRtI0Sefkx7wSWCBpIXAVaQzEBcTMbAgNShdWXyLiAeAtPcxfAByab/8OePUgp2ZmZn3ohBaImZl1IRcQMzOrxAXEzMwqcQExM7NKXEDMzKwSFxAzM6vEBcTMzCpxATEzs0pcQMzMrBIXEDMzq8QFxMzMKnEBMTOzSlxAzMysEhcQMzOrxAXEzMwqcQExM7NKXEDMzKwSFxAzM6vEBcTMzCpxATEzs0pcQMzMrBIXEDMzq8QFxMzMKnEBMTOzSlxAzMysEhcQMzOrxAXEzMwqcQExM7NKXEDMzKwSFxAzM6vEBcTMzCpxATEzs0pcQMzMrBIXEDMzq8QFxMzMKnEBMTOzSlxAzMysEhcQMzOrxAXEzMwqcQExM7NKXEDMzKwSFxAzM6vEBcTMzCpxATEzs0pcQMzMrBIXEDMzq2TIC4ik/SQtkrRS0rQ+Hre7pFslLZF07GDmaGZmqxryAgLcCOwDXNPbAySNBM4E9gCmAO+RNGVw0jMzs56MGuoEIuJmAEl9PWwHYElELM2PnQvMBG5qe4JmZtajIS8gJW0A3FmYXgbs2NMDJc0GZufJ5ZJurTmXtYH7OzBW3fE6Obe643VybnXH6+Tc6o7n3Kp7WZkHDUoBkfQrYN0e7vpMRFxS52tFxNnA2XXGLJK0ICJ6HasZqlh1x+vk3OqO18m51R2vk3OrO55za79BKSARscsAQ9wFTC5Mb5jnmZnZEOmEQfQyrgO2kLSJpNHAAcC8Ic7JzGxYG/ICImlvScuA1wI/l3R5nr++pMsAImIFcBhwOXAzcFFELBqilOvsHqu7q2245FZ3vE7Ore54nZxb3fGcW5spIobidc3MrMsNeQvEzMy6kwuImZlV4gLSpdTPPy9faIbT8g6nZbXu5gIyRAa6kYjC4FWnbnAk1fb5ioioczkljezU9y1qHJiUtJakiXUtq6QxNcbaOF935HqQtLGkTfLtjsox/8ho0lDn4QLSD0kj6vjwSBov6V2SJsPACoCkXSUdJullxVjKKuQ2RtKOktZs9bl9iYiVdcSR9GZJW9a5YY2IZ+qKl7/M69T0OdlT0rgai++RwP65AI+sId5ngN3g2WPUVZKf+w1JG+bcBry8kj4raYeB5lZwHPA1Serts1J2nUvaR9I6rTynH58BPt/Pa7a96LmA9CMiVhY20AN5v95E+iny5yQdlTeKa+XXeLYAlIz1WmA6cKqkUyTNlLRmZC3GAngH8FXg6FzktpQ0voXnr0LSHEmzBhKj4IPAp3J9rGNDc5SkkySNqulLNgf4YF+tpDKvk5ftaOB1EbGy+JzG7Qr5PkBarxtHxDOF16lqDeATkkY04lU0Fnga+BLUtrPxSuAjOd5AckPSasD+wBuBj/X2uDI7IZJGARcDn+jtOa2s15zbbOAQSe8cSG4D5QLSC0nbSloo6XhJ28HzP+QVvoQB/DtwH+k4Xh8Fvijpw5KmSRpf8sM4hVSIvgvMB1YHDga+KenzknaWtFqLH54NgR8CG5H2WL8EHCHprZJelj+wVXxQ0no575H5usoG+yRgM2DPmjY0HyK9/9vVtGd+C3C4pJ0LBfx5MUuuD5H+63SOpM2LOwON261uFCLiP0ifk4slrZvnrZS0em4Vz5E0oYWQnwRWA+ZKGtPIr5Wccg6PkTaor5N0UmP+AFv8RwPbSzqlEK9qrEOB3wE7kwrm1s0PyDshq5eINQt4ApgpaWZPD2hxvR4C/BZ4F/BV5a7AptyObHG9VhMRvvRwAV4FHAN8C/hv4OfAx4GXVYi1GfA3YOs8vQnwfuAbwE+AC4GzgM1KxJqQn3NkIdZewGeB84FLgQuAkSVz2wp4DHh/YbmPBS4DrgbOI30xJ7W4zGvlXE7v5f71S8Zp/Ffpw8AdwE6F+0Y27m8hr2nA/wHHA9c03TciX29UYR1/knRqgi0K8zbMlxOBF7UQ61zgZ8DaeXoi8Pr8HpxSIbeRwPfyMs/Mn7efk1onF7QQZ3S+Xhe4BNi7t/VVJqfC5+9iUqtrIN/X1fL1q0kFc8YA4/0JmJVvXwB8q+k92Bm4p2SsG4A9SUXpz8BLSDsLjffgdcBpLeZ2UL59GfCVfHtsvn4D6ejllZe/dC6D8SLddslfuPcDU4FtgLeT+hx/DPwe+E7+MIzt7wtT2AAeR9rwj226/+WkLprzGl+CEvm9CVgITC/MGwFsSWqNHNjCsp4NLAF+DWzcdN9OwGnAlS3kpsLt9XPsT5HO4/IGUtH8PnAvMKbF9XIyqaX02gGs2283NsKklsOJTfe/CPhHq7nl534vfzY+DlxB2vG4FzirhRgTgHVIR58+F7gqf+ZuJxXkVTbavcQZTdqx+Fh+3sPASuCXwBeA95JanOu0uIwbkY7U+hfgf4DPkcZEXtpinLXyhvMw4BlgEfAfwH60uLNSiPkSUrG9Drg+L+NWwMQW46wPPFCY3gZYCswszJsLfLVkrEca3w3gV8AnG+soX/8Q+GYLuT1YmJ6Rc9uhMO9CKuxoVLn4n+g9kLQB8F+kD/bvSd0KS0lfyk2BbUkb8Q9ExG0lY25EKhKLIuKI3PT9J2mP+DXAkxFxTgs5zgE+DbwTuDEi/lm4b0SU7OqR9ADwFuAo0kZzv2IMSW8Bto2Ik8vmlp+/EzCJ1Ce9K+n9ewL4DWlj+JPI53fpI8bapH7tA0lddXvl5z5J2iBeCVwa+ZwyJfO6H3hTRCyStCvwNeAgYEFEhKQjgXdExIwSscYBHwDWI40jvRjYGPhFvvyJdOidpyN12fQV662kY7ytn5f5HtLG+v/lZbxW0piIeKrkcs4h7Zg8RSpsd5C6Tj9EaiU9USZOId6BpA3y2vlyCWk8ZBwwJue7GPh68bPYS6xfk8Y/ppDW4V9JO22TSadumAD8ONKRtcvk9lbS92DTHPMKUpEbDTxI2uu/gfQ+9js2krvUto+It0gaGRHPSDqc1DLfMSLulPQQ6Xvxt35inQBMiYh98vQ7ga8Du8Zz50J6MMe6o2Ru20XEboXcTia1cKZFxONlc6vFYFSpbr0Aa5IGSG8E/gCcALwZ2DqvxFbj7U/qPjmHVEweIDW3r84rv7/nTyC1ehrN4btI/bQfIjXd1yB3w5TMZy/glnx7I9J5Vubk6VH5eikl93rz43cC7iYV3oWklttZpDGb8S2+X9/KMU4H/oXUXbcFsAvpy/wz4IoW4s0sLO9qpI3WNyh045BOUvaukvHeR+qLvii/lzvkdXE/LXaDAaeQitkBpFbpusBXSHvSLe1B53hHsWqLUqTumLNJLdZRLcQ7gtSy2ppCa4NU8PYjFbovl4izJakl9J48PbZw37qknY0TgNe3kNud+Tu1B6m7uNGVsympBXYl8I0W4h0IrFv8HuTbl5C6it8N3FQy1t+blyW/V9fm2/sBf2kht2OAzRuf4cZ7SNoOzMm5LWr181L1Migv8kK45I3XicCt+Uu9fcnn7UVqov4G+COpaPwT+Le8MSzVhZA3dj8ibeTnk/qw35s3MjeQugB+StrzKLtMVwLHFqYPJjX/18vTW1BoypeM+Yb8RW58AUeQ9gZvBk5oIc7I/GV5Yy/3TyB1T2zdQswvAoc34heWcRmpGKxBoXugRLy30UPBzuvkItKeeb8FndTiuLuX+34AnNriOtgKeBw4qrAOGuM7U/LG5oAW4m1G2ki/qjBvBE3dt8CLS8SaQOr+OSZPj6KFQtZDvCmkgvS+wjz1kNvaJeNtThqvnN4cC9ietMPwD+DDJWJtmb/r4xqx8vVY0o7R3qQuxX9tYb0+BhxdyK2xXnfPsZYBH636frb8/g/WC71QLvmLsyOwRsnH/oE0wPp+UtN/DVJf7xmFx/U78EjqFz8sfyhX2ZMnDepdCLyy5HKMyl+UNfP0anmD93PygB5wKvC9Ft+bg0gb5bEUBvJJ40mLyXueJWKtT+pnv4E0rrAvaY+ypVZMU277klpq4yhs2Ek/ibyG1G1ZannzhuYO4M2F+MqXyXlD88mSsSaQWlPHF9ZFo8DtQOriKdUqys9pjGtdQf7RR9PyHgI8RIlxrcJG7wukMbyWx4Z6iDmd1K00vYd1VLoFXVjWm0k7Qz0ta6mxux6W9Yc9LStpJ+QZclEosV5/AhyXp0cV1ut+wG2kQt9vrKb1enkvy3phzm1smXh1XAblRXx5dgU3PqBTSHt0xw0wzghK/tqqhxhjya2opg/h60l7WDsB/0sLA9ak/uu/krqBvpU32JuQu2BIe/nzKVF8CzHXJG3g/0oaUziZ1I24QYsbhw1IXZGLSN2HjdzG5/u/SdqTfU0L739fG5qdSP3vo0vm98a8fNN7uO9o4PstLOsDpHG17wIXF+Y3uiX3Br7W4udlI9IA8Ol5ejypEO9B+kPbrBbjzSEV4G1osWj0sqzfaVrWxob6veRW5wCXdTyp8H2WNM5TNlaP6zV//y4FflHjep1FOtVFpfey0vs/mC82nC+s2qTekdQVtktN8Vv+SWsfsT4GLAfuqPj85o3+KXmjP4VeftZbMu7GpP7xW3MxaPnXWD3kdmrO7W200NrKsXrbqO6eN/qfazFerxtVYELJGH2NazU2qrfRwrhWIXZPY3i/Ju3999ulS99jeFsBq7eYT5llXQzsU9OyXp2Xt1T3dcn1WmpnquSy3kILLdU6LoP2Qr4878PQWOFn0OLe0SDlNy5vGAecW2Gjv5g0sF56zKKPmCNIXTulWzL95HYrqWW0VYUYPW1orsrxBvrDiK1Iv+wq3cqk5nEthtEYXl3LWnK9rkELO3wll7X0+F1dF/+Mdwjlf/KujH5+9jgUJL0EeDxa/LlnH/FGkAYhb42Ih+uIWZec2w6kPbx+c5O0F+nnu5NI40abkf4/cjKpiDwcEfeViDOSNNi+I6lv+zHST25fQ/pvxWqk1sIXI+LPJeKNynG2jYiH8hEERpD+v7Q4Io6UdCrpfxYHlog3glT0f0QqkpcBK0j/aRoREYfnx/V6rKhCrHVIvxD6FfC/EfF40/07k8b4josSP8vu8GUts16X5GUd9PVaq8GuWL740s0XOvuHEbWPazXFf0GP4dW1rN22XgdycQvEbAAae6T5GGWXA+dGxHEDiNP4eeyADgbYQ/yPkbpiHoiIl1XNrzC9I+k/NMdExK9qyG8kqTU+4A1SJy1rp6/XgfLBFM0qajrI4U2kX3btJWmXVmMV4qyM546aW+c5S84BriX9oKFlTRvUkRHxB9KhWqbUkVzUeHh9OmhZO329DpRbIGY1KBxW4gzSgezOGOqcmrVhXGs4jeENm2Vt6bVdQMzq08kbGrO6uYCYmVklHgMxM7NKXEDMzKwSFxAzM6vEBcSsA0n6dj4ZEUrnub91qHMya+YCYjZAkv4m6QlJyyXdkzf+E+uKHxG/iYhX1BXPrC4uIGb12CsiJgLbkU5T/Nkhzses7VxAzGoUEXeRzoe+laSDJd0s6VFJS/N5ygGQNEvSb4vPlRSSNm+OKWm6pGXtz96sNS4gZjWSNJl0CO8/A/cCbycdqfdg4DRJ2w1hema1GjXUCZi9QPxU0grgEdK5Lr7cdGiJqyVdQToS65+GIkGzurmAmNXjnc1HapW0B+m0ty8ntfbHk86EaPaC4C4sszbIx8T6EekkU5MiYg3SSYoaR2F9jFRQGo9fd9CTNBsgFxCz9hhNOlvhfcCK3BrZrXD/QuBVkl4jaSzpzHdmXcUFxKwNIuJR4HDSqU0fIp3/e17h/sXA8aRTvN4G/LaHMGYdzUfjNTOzStwCMTOzSlxAzMysEhcQMzOrxAXEzMwqcQExM7NKXEDMzKwSFxAzM6vEBcTMzCra+bhVAAAABklEQVT5/9ZIGoWYRiHUAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -367,7 +457,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -379,9 +469,9 @@ }, { "data": { - "image/png": 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U+yvX6l/FpI2ZIYfbQJyqqtixYweAaz+WiDIx0JDhYrFY8t+yLFseKHhQoHJL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\noDR5IHc3QC2yMvCiRUnxgnzCbFhX/ZtyyPzRMTQ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97W/7HgOTSqUYbI92I9Cgt5TG0/i1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\n0AAAAOMRaAAAgPEINAAAwHgEGgAAYDwCDQAAMB6BBgAAGI9AAwAAjEe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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -394,14 +484,14 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { - "image/png": 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SGy+fz2NsbAzhcLjCwiQ3qRmYqXdAnDbJZBI9PT1ViRbYm2WrqiqmpqZQLBZx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\nO5GpTZDZEm5KDAcArJptZmaGVRZ6vV5ZU8hC7ZJnm7+9rzHbXK1xXn3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YLCgrK1Pki1ss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\nHwE8kQ14THbpAAAAAElFTkSuQmCC\n", + "image/png": 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\n", 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RSNJux42pqSk4nU50d3ejvb3dlAf/MFm2jdRIyXUi3Rj02sWTDMCDyEo8LHig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9GIjo6OovG9YpxiNBrF+vo6amtr0d3dva3j+nw+DA4OoqqqivEpCavlzWw2s2IHALj99ttxww03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\nM/g8/q8PpnQAAAAASUVORK5CYII=\n", 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\n", 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whYVJblIzMFPvgDhtkskkenp6qhItsDPLVlVVTExMoFgs4uLFixURFLu5+bPZ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OwsgBz1Ti0RWIgypgbbzM3NQa/Xo6urS/a5eFzBYBATExPQ6XJ8246ODlV2gSRJGBsbg8lkkh2v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\nEokMfoBLSkrg6+uLwsJCTJkyBZGRkb2y4dOfsLS0x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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -434,21 +514,48 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "n = 2 # number of qubits \n", + "q = QuantumRegister(\"q\", n)\n", + "c = ClassicalRegister(\"c\", n)\n", + "\n", + "qc2 = QuantumCircuit(q, c)\n", + "qc2.h(q[1])\n", + "qc2.z(q[1])\n", + "\n", + "\n", + "# execute the quantum circuit \n", + "qp = QuantumProgram()\n", + "qp.add_circuit(\"neg_superposition\", qc2)\n", + "circuits = ['neg_superposition']\n", + "backend = 'local_unitary_simulator' # the device to run on\n", + "result = qp.execute(circuits, backend=backend, shots=1000)\n", + "ground = np.zeros(2**n)\n", + "ground[0]=1.0\n", + "state_neg_superposition = np.dot(result.get_data('neg_superposition')['unitary'], ground)\n", + "rho_neg_superposition=state_2_rho(state_neg_superposition)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The 0th eigenvalue = 0.75\n" + "The 0th eigenvalue = 0.5000000000000001\n" ] }, { "data": { - "image/png": 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0ZIlPP/0UALB161abS+Kcg1C+5XBKuemmYoccO7cBow16zSSKIvx+P4B4Wxqi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\nrkJggg==\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -458,14 +565,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "The 1th eigenvalue = 0.25\n" + "The 1th eigenvalue = 0.4999999999999999\n" ] }, { "data": { - "image/png": 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97NIqVu+M4/L9lmv1t2LSxsyQw20gRgiBbdu2Abj9ZYloNgYaMlwkEkn8rCiK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\nAAAwHoEGAAAYj0ADAACMR6ABAADGI9AAAADjEWgAAIDxCDQAAMB4BBo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+ "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -473,22 +580,22 @@ } ], "source": [ - "plot_state(rho_superposition*.5+rho_ghz*.5,'qsphere')" + "plot_state(0.5*rho_neg_superposition + 0.5* rho_superposition, 'qsphere')" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Version information

\n", - "

Please note that this tutorial is targeted to the stable version of the QISKit SDK. The following versions of the packages are recommended:

\n", + "

Please note that this tutorial is targeted to the stable version of the QISKit. The following versions of the packages are recommended:

\n", "
PackageVersion
QISKit 0.4.8
QISKit 0.4.10
IBMQuantumExperience>= 1.8.26
numpy>= 1.13, < 1.14
scipy>= 0.19, < 0.20
\n", "\n", - "\n", + "\n", "\n", "\n", "\n", @@ -504,15 +611,13 @@ } ], "source": [ - "%run \"../version.ipynb\"" + "%run \"../../version.ipynb\"" ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [] } @@ -534,7 +639,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.6.4" } }, "nbformat": 4, diff --git a/reference/tools/working_with_backends.ipynb b/reference/tools/working_with_backends.ipynb index f417268d1..1f9c41086 100644 --- a/reference/tools/working_with_backends.ipynb +++ b/reference/tools/working_with_backends.ipynb @@ -54,23 +54,43 @@ "if sys.version_info < (3,5):\n", " raise Exception('Please use Python version 3.5 or greater.')\n", " \n", - "from pprint import pprint\n", - "\n", - "# import QISKit\n", - "from qiskit import QuantumProgram\n", - "import Qconfig\n", - "\n", - "# import basic plotting tools\n", - "from qiskit.tools.visualization import plot_histogram" + "try:\n", + " sys.path.append(\"../../\") # go to parent dir\n", + " import Qconfig\n", + " qx_config = {\n", + " \"APItoken\": Qconfig.APItoken,\n", + " \"url\": Qconfig.config['url']}\n", + "except:\n", + " qx_config = {\n", + " \"APItoken\":\"YOUR_TOKEN_HERE\",\n", + " \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}" ] }, { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], + "source": [ + "from qiskit import QuantumProgram\n", + "from qiskit.tools.visualization import plot_histogram\n", + "from pprint import pprint" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:710: DeprecationWarning: set_api() will be deprecated in upcoming versions (>0.5.0). Using the API object instead is recommended.\n", + " \"Using the API object instead is recommended.\", DeprecationWarning)\n" + ] + } + ], "source": [ "Q_program = QuantumProgram()\n", "Q_program.set_api(Qconfig.APItoken, Qconfig.config['url']) # set the APIToken and API url" @@ -87,20 +107,32 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:797: DeprecationWarning: available_backends() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.local_backends() and qiskit.backends.remote_backends() instead is recommended.\n", + " DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "['ibmqx5',\n", - " 'ibmqx4',\n", - " 'ibmqx_hpc_qasm_simulator',\n", + "['local_qasm_simulator',\n", + " 'local_clifford_simulator',\n", + " 'local_qiskit_simulator',\n", + " 'local_sympy_qasm_simulator',\n", + " 'local_sympy_unitary_simulator',\n", + " 'local_unitary_simulator',\n", " 'ibmqx2',\n", - " 'ibmqx_qasm_simulator',\n", - " 'local_qasm_simulator',\n", - " 'local_unitary_simulator']\n" + " 'ibmqx5',\n", + " 'ibmqx_hpc_qasm_simulator',\n", + " 'ibmqx4',\n", + " 'ibmqx_qasm_simulator']\n" ] } ], @@ -117,14 +149,22 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:911: DeprecationWarning: get_backend_status() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').status instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "{'available': True, 'busy': False, 'pending_jobs': 46}\n" + "{'available': True, 'backend': 'ibmqx5', 'busy': False, 'pending_jobs': 0}\n" ] } ], @@ -141,14 +181,22 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:911: DeprecationWarning: get_backend_status() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').status instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "{'available': True, 'busy': False, 'pending_jobs': 0}\n" + "{'available': True, 'backend': 'ibmqx2', 'busy': False, 'pending_jobs': 0}\n" ] } ], @@ -177,17 +225,26 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:941: DeprecationWarning: get_backend_configuration() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').configuration instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ "{'basis_gates': 'u1,u2,u3,cx,id',\n", " 'chip_name': 'Sparrow',\n", - " 'coupling_map': {0: [1, 2], 1: [2], 3: [2, 4], 4: [2]},\n", + " 'coupling_map': [[0, 1], [0, 2], [1, 2], [3, 2], [3, 4], [4, 2]],\n", " 'description': '5 transmon bowtie',\n", + " 'local': False,\n", " 'n_qubits': 5,\n", " 'name': 'ibmqx2',\n", " 'online_date': '2017-01-10T12:00:00.000Z',\n", @@ -203,9 +260,17 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:941: DeprecationWarning: get_backend_configuration() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').configuration instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -213,6 +278,7 @@ "{'basis_gates': 'u1,u2,u3,cx,id',\n", " 'coupling_map': 'all-to-all',\n", " 'description': 'A python simulator for qasm files',\n", + " 'local': True,\n", " 'name': 'local_qasm_simulator',\n", " 'simulator': True,\n", " 'url': 'https://github.com/IBM/qiskit-sdk-py'}\n" @@ -234,14 +300,22 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:970: DeprecationWarning: get_backend_calibration() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').calibration instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "{'last_update_date': '2018-03-12T11:38:29.000Z', 'qubits': [{'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.000858490762927322}, 'name': 'Q0', 'readoutError': {'date': '2018-03-12T11:38:29Z', 'value': 0.046}}, {'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.0006867731322012238}, 'name': 'Q1', 'readoutError': {'date': '2018-03-12T11:38:29Z', 'value': 0.054}}, {'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.00197489316929661}, 'name': 'Q2', 'readoutError': {'date': '2018-03-12T11:38:29Z', 'value': 0.128}}, {'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.00197489316929661}, 'name': 'Q3', 'readoutError': {'date': '2018-03-12T11:38:29Z', 'value': 0.087}}, {'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.001803112096824766}, 'name': 'Q4', 'readoutError': {'date': '2018-03-12T11:38:29Z', 'value': 0.045}}], 'multi_qubit_gates': [{'qubits': [1, 0], 'type': 'CX', 'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.019933034541237543}, 'name': 'CX1_0'}, {'qubits': [2, 0], 'type': 'CX', 'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.024806261843678845}, 'name': 'CX2_0'}, {'qubits': [2, 1], 'type': 'CX', 'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.0584889238863901}, 'name': 'CX2_1'}, {'qubits': [2, 4], 'type': 'CX', 'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.06398473494573023}, 'name': 'CX2_4'}, {'qubits': [3, 2], 'type': 'CX', 'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.02677371835866532}, 'name': 'CX3_2'}, {'qubits': [3, 4], 'type': 'CX', 'gateError': {'date': '2018-03-12T11:38:29Z', 'value': 0.0248740607207448}, 'name': 'CX3_4'}], 'backend': 'ibmqx4'}\n" + "{'last_update_date': '2018-04-15T10:47:03.000Z', 'qubits': [{'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.0012019552727863259}, 'name': 'Q0', 'readoutError': {'date': '2018-04-15T10:47:03Z', 'value': 0.049}}, {'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.0006867731322012238}, 'name': 'Q1', 'readoutError': {'date': '2018-04-15T10:47:03Z', 'value': 0.032}}, {'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.0014595792651160289}, 'name': 'Q2', 'readoutError': {'date': '2018-04-15T10:47:03Z', 'value': 0.051}}, {'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.003779185579426747}, 'name': 'Q3', 'readoutError': {'date': '2018-04-15T10:47:03Z', 'value': 0.318}}, {'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.002662115274625232}, 'name': 'Q4', 'readoutError': {'date': '2018-04-15T10:47:03Z', 'value': 0.058}}], 'multi_qubit_gates': [{'qubits': [1, 0], 'type': 'CX', 'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.03024023736391171}, 'name': 'CX1_0'}, {'qubits': [2, 0], 'type': 'CX', 'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.039456925451956476}, 'name': 'CX2_0'}, {'qubits': [2, 1], 'type': 'CX', 'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.031533820743726626}, 'name': 'CX2_1'}, {'qubits': [3, 2], 'type': 'CX', 'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.07034276934905859}, 'name': 'CX3_2'}, {'qubits': [3, 4], 'type': 'CX', 'gateError': {'date': '2018-04-15T10:47:03Z', 'value': 0.07835000865792408}, 'name': 'CX3_4'}], 'backend': 'ibmqx4'}\n" ] } ], @@ -251,14 +325,22 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:1000: DeprecationWarning: get_backend_parameters() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').parametersinstead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "{'last_update_date': '2018-03-12T11:38:29.000Z', 'fridge_parameters': {'cooldownDate': '2017-09-07', 'Temperature': {'date': '2018-03-12T11:38:29Z', 'value': 0.021, 'unit': 'K'}}, 'qubits': [{'name': 'Q0', 'buffer': {'date': '2018-03-12T11:38:29Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-03-12T11:38:29Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-03-12T11:38:29Z', 'value': 35.4, 'unit': 'µs'}, 'T1': {'date': '2018-03-12T11:38:29Z', 'value': 55.4, 'unit': 'µs'}, 'frequency': {'date': '2018-03-12T11:38:29Z', 'value': 5.24466, 'unit': 'GHz'}}, {'name': 'Q1', 'buffer': {'date': '2018-03-12T11:38:29Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-03-12T11:38:29Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-03-12T11:38:29Z', 'value': 61.7, 'unit': 'µs'}, 'T1': {'date': '2018-03-12T11:38:29Z', 'value': 55.3, 'unit': 'µs'}, 'frequency': {'date': '2018-03-12T11:38:29Z', 'value': 5.30492, 'unit': 'GHz'}}, {'name': 'Q2', 'buffer': {'date': '2018-03-12T11:38:29Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-03-12T11:38:29Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-03-12T11:38:29Z', 'value': 38, 'unit': 'µs'}, 'T1': {'date': '2018-03-12T11:38:29Z', 'value': 39.3, 'unit': 'µs'}, 'frequency': {'date': '2018-03-12T11:38:29Z', 'value': 5.35192, 'unit': 'GHz'}}, {'name': 'Q3', 'buffer': {'date': '2018-03-12T11:38:29Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-03-12T11:38:29Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-03-12T11:38:29Z', 'value': 12.6, 'unit': 'µs'}, 'T1': {'date': '2018-03-12T11:38:29Z', 'value': 47.6, 'unit': 'µs'}, 'frequency': {'date': '2018-03-12T11:38:29Z', 'value': 5.43031, 'unit': 'GHz'}}, {'name': 'Q4', 'buffer': {'date': '2018-03-12T11:38:29Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-03-12T11:38:29Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-03-12T11:38:29Z', 'value': 32.1, 'unit': 'µs'}, 'T1': {'date': '2018-03-12T11:38:29Z', 'value': 58.7, 'unit': 'µs'}, 'frequency': {'date': '2018-03-12T11:38:29Z', 'value': 5.18388, 'unit': 'GHz'}}], 'backend': 'ibmqx4'}\n" + "{'last_update_date': '2018-04-15T10:47:03.000Z', 'fridge_parameters': {'cooldownDate': '2017-09-07', 'Temperature': {'date': '2018-04-15T10:47:03Z', 'value': 0.021, 'unit': 'K'}}, 'qubits': [{'name': 'Q0', 'buffer': {'date': '2018-04-15T10:47:03Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-04-15T10:47:03Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-04-15T10:47:03Z', 'value': 16.5, 'unit': 'µs'}, 'T1': {'date': '2018-04-15T10:47:03Z', 'value': 45.2, 'unit': 'µs'}, 'frequency': {'date': '2018-04-15T10:47:03Z', 'value': 5.24208, 'unit': 'GHz'}}, {'name': 'Q1', 'buffer': {'date': '2018-04-15T10:47:03Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-04-15T10:47:03Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-04-15T10:47:03Z', 'value': 58.3, 'unit': 'µs'}, 'T1': {'date': '2018-04-15T10:47:03Z', 'value': 48.7, 'unit': 'µs'}, 'frequency': {'date': '2018-04-15T10:47:03Z', 'value': 5.30743, 'unit': 'GHz'}}, {'name': 'Q2', 'buffer': {'date': '2018-04-15T10:47:03Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-04-15T10:47:03Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-04-15T10:47:03Z', 'value': 64.5, 'unit': 'µs'}, 'T1': {'date': '2018-04-15T10:47:03Z', 'value': 39.6, 'unit': 'µs'}, 'frequency': {'date': '2018-04-15T10:47:03Z', 'value': 5.35152, 'unit': 'GHz'}}, {'name': 'Q3', 'buffer': {'date': '2018-04-15T10:47:03Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-04-15T10:47:03Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-04-15T10:47:03Z', 'value': 19.8, 'unit': 'µs'}, 'T1': {'date': '2018-04-15T10:47:03Z', 'value': 34.7, 'unit': 'µs'}, 'frequency': {'date': '2018-04-15T10:47:03Z', 'value': 5.41313, 'unit': 'GHz'}}, {'name': 'Q4', 'buffer': {'date': '2018-04-15T10:47:03Z', 'value': 10, 'unit': 'ns'}, 'gateTime': {'date': '2018-04-15T10:47:03Z', 'value': 50, 'unit': 'ns'}, 'T2': {'date': '2018-04-15T10:47:03Z', 'value': 25.7, 'unit': 'µs'}, 'T1': {'date': '2018-04-15T10:47:03Z', 'value': 47.3, 'unit': 'µs'}, 'frequency': {'date': '2018-04-15T10:47:03Z', 'value': 5.18919, 'unit': 'GHz'}}], 'backend': 'ibmqx4'}\n" ] } ], @@ -281,7 +363,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -323,9 +405,17 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:941: DeprecationWarning: get_backend_configuration() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').configuration instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -334,8 +424,10 @@ "include \"qelib1.inc\";\n", "qreg q[2];\n", "creg c2[2];\n", - "u2(0.0,3.141592653589793) q[0];\n", + "u2(0,3.14159265358979) q[0];\n", "cx q[0],q[1];\n", + "barrier q[1];\n", + "barrier q[0];\n", "measure q[1] -> c2[1];\n", "measure q[0] -> c2[0];\n", "\n" @@ -361,9 +453,17 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jaygambetta/miniconda3/envs/QISKitenv/lib/python3.6/site-packages/qiskit/_quantumprogram.py:941: DeprecationWarning: get_backend_configuration() will be deprecated in upcoming versions (>0.5.0). Using qiskit.backends.get_backend_instance('name').configuration instead is recommended.\n", + " \"instead is recommended.\", DeprecationWarning)\n" + ] + }, { "name": "stdout", "output_type": "stream", @@ -372,10 +472,16 @@ "include \"qelib1.inc\";\n", "qreg q[2];\n", "creg c2[2];\n", - "u2(0.0,3.141592653589793) q[1];\n", + "u2(0,3.14159265358979) q[1];\n", "cx q[1],q[0];\n", - "measure q[0] -> c2[1];\n", - "measure q[1] -> c2[0];\n", + "u2(0,3.14159265358979) q[0];\n", + "barrier q[0];\n", + "barrier q[0];\n", + "measure q[0] -> c2[0];\n", + "u2(0,3.14159265358979) q[1];\n", + "barrier q[1];\n", + "barrier q[1];\n", + "measure q[1] -> c2[1];\n", "\n" ] } @@ -401,14 +507,14 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -422,14 +528,14 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -443,11 +549,33 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "

Version information

\n", + "

Please note that this tutorial is targeted to the stable version of the QISKit. The following versions of the packages are recommended:

\n", + "
PackageVersion
QISKit 0.4.8
QISKit 0.4.10
IBMQuantumExperience>= 1.8.26
numpy>= 1.13, < 1.14
scipy>= 0.19, < 0.20
\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
PackageVersion
QISKit 0.4.10
IBMQuantumExperience>= 1.8.26
numpy>= 1.13, < 1.14
scipy>= 0.19, < 0.20
matplotlib>= 2.0, < 2.1
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "#%run \"../version.ipynb\"" + "%run \"../../version.ipynb\"" ] } ],