🧪 Initializing |0⟩ and |1⟩

This task sheet accompanies the notebook Qiskit_qubit_measure.ipynb.
In this lab, we explored how to prepare and measure the basis states of a qubit:

• |0⟩ (default starting state)
• |1⟩ (using an X gate to flip the qubit)

We used the AerSimulator in Qiskit to run the experiments.

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✅ Tasks

Task 1: Verify |0⟩ and |1⟩

1. Run the given program for |0⟩ and |1⟩.
2. Record the counts for 512 shots.
3. Question: Are the results deterministic or random? Why?

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Task 2: Change the number of shots

1. Modify the code to run with 10 shots and 1000 shots.
2. Observe the results. Do they change? Why or why not?

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Task 3: Superposition with Hadamard

1. Modify the circuit to apply a Hadamard (H) gate before measurement:

   qc = QuantumCircuit(1, 1)
   qc.h(0)
   qc.measure_all()

2. Run with 512 shots.
3. Question: What outcomes do you see? Are they deterministic or probabilistic?

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Task 4: Combine X and H gates

1. Create a circuit that applies X followed by H:

   qc.x(0)
   qc.h(0)
   qc.measure_all()

2. Run with 512 shots.
3. Predict the results before running: what distribution do you expect?
   (Hint: Think about how H acts on |1⟩).

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Task 5 (Challenge)

• Build a 2-qubit circuit where:
  • Qubit 0 is |0⟩
  • Qubit 1 is |1⟩
• Measure both.
• Run with 512 shots.
• Question: What outputs do you expect? Does the simulator confirm it?

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📝 Notes

• Remember:
  • Qubits start in |0⟩.
  • X flips |0⟩ ↔ |1⟩.
  • H creates superposition.
  • Measurement collapses the qubit into 0 or 1.