Introduce FSIM gates and 2Q Pauli Rotations

This PR makes the stdgates.quil consistent with the QuilC stdgates

Author: bramathon

quil/stdgates.quil

@@ -130,8 +130,77 @@ DEFGATE ISWAP:
     0, i, 0, 0
     0, 0, 0, 1
 
+DEFGATE SQISWAP:
+    1, 0,         0,         0
+    0, 1/sqrt(2), i/sqrt(2), 0
+    0, i/sqrt(2), 1/sqrt(2), 0
+    0, 0,         0,         1
+
+
 DEFGATE PSWAP(%theta):
     1, 0,           0,           0
     0, 0,           cis(%theta), 0
     0, cis(%theta), 0,           0
     0, 0,           0,           1
+
+## 2-Qubit Pauli rotation gates
+
+DEFGATE RZZ(%phi):
+    cis(-%phi/2), 0,             0,             0
+    0,              cis(%phi/2), 0,             0
+    0,              0,             cis(%phi/2), 0
+    0,              0,             0,             cis(-%phi/2)
+
+DEFGATE RXX(%phi):
+    cos(%phi/2),    0,              0,              -i*sin(%phi/2)
+    0,              cos(%phi/2),    -i*sin(%phi/2), 0
+    0,              -i*sin(%phi/2), cos(%phi/2),    0
+    -i*sin(%phi/2), 0,              0,              cos(%phi/2)
+
+DEFGATE RYY(%phi):
+    cos(%phi/2),    0,              0,              i*sin(%phi/2)
+    0,              cos(%phi/2),    -i*sin(%phi/2), 0
+    0,              -i*sin(%phi/2), cos(%phi/2),    0
+    i*sin(%phi/2), 0,              0,              cos(%phi/2)
+
+## Fermionic Simulation gates
+
+DEFGATE FSIM(%theta, %phi):
+    1, 0,               0,               0
+    0, cos(%theta/2),   i*sin(%theta/2), 0
+    0, i*sin(%theta/2), cos(%theta/2),   0
+    0, 0,               0,               cis(%phi)
+
+DEFGATE PHASEDFSIM(%theta, %zeta, %chi, %gamma, %phi):
+    1, 0,                                       0,                                       0
+    0, cis(-%gamma - %zeta)*cos(%theta/2),  i*cis(%chi - %gamma)*sin(%theta/2), 0
+    0, i*cis(-%gamma - %chi)*sin(%theta/2), cis(%zeta - %gamma)*cos(%theta/2),  0
+    0, 0,                                       0,                                       cis(%phi - 2*%gamma)
+
+## Lesser-known standard gates
+
+DEFGATE PISWAP(%theta):
+    1, 0,               0,               0
+    0, cos(%theta/2),   i*sin(%theta/2), 0
+    0, i*sin(%theta/2), cos(%theta/2),   0
+    0, 0,               0,               1
+
+# there has been some internal debate about whether this gate should be parameterized
+# by -1.0*%theta instead. we seem to have picked this one for good, but it's still
+# not 100% clear to me that this is the "right" move.
+DEFGATE XY(%theta):
+    1, 0,               0,               0
+    0, cos(%theta/2),   i*sin(%theta/2), 0
+    0, i*sin(%theta/2), cos(%theta/2),   0
+    0, 0,               0,               1
+
+DEFGATE CAN(%alpha, %beta, %gamma):
+    (cis((%alpha+%beta-%gamma)/2)+cis((%alpha-%beta+%gamma)/2))/2, 0, 0, (cis((%alpha-%beta+%gamma)/2)-cis((%alpha+%beta-%gamma)/2))/2
+    0, (cis((%alpha+%beta+%gamma)/(-2))+cis((%beta+%gamma-%alpha)/2))/2, (cis((%alpha+%beta+%gamma)/(-2))-cis((%beta+%gamma-%alpha)/2))/2, 0
+    0, (cis((%alpha+%beta+%gamma)/(-2))-cis((%beta+%gamma-%alpha)/2))/2, (cis((%alpha+%beta+%gamma)/(-2))+cis((%beta+%gamma-%alpha)/2))/2, 0
+    (cis((%alpha-%beta+%gamma)/2)-cis((%alpha+%beta-%gamma)/2))/2, 0, 0, (cis((%alpha+%beta-%gamma)/2)+cis((%alpha-%beta+%gamma)/2))/2
+
+DEFGATE BLOCH(%alpha, %beta, %gamma) q AS PAULI-SUM:
+    X(%alpha) q
+    Y(%beta) q
+    Z(%gamma) q