/
stdgates.quil
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stdgates.quil
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### Quil standard gate defintions.
## Pauli Gates
DEFGATE I:
1, 0
0, 1
DEFGATE X:
0, 1
1, 0
DEFGATE Y:
0, -i
i, 0
DEFGATE Z:
1, 0
0, -1
## Hadamard Gate
DEFGATE H:
1/sqrt(2), 1/sqrt(2)
1/sqrt(2), -1/sqrt(2)
## Cartesian Rotation Gates
DEFGATE RX(%theta):
cos(%theta/2), -i*sin(%theta/2)
-i*sin(%theta/2), cos(%theta/2)
DEFGATE RY(%theta):
cos(%theta/2), -sin(%theta/2)
sin(%theta/2), cos(%theta/2)
DEFGATE RZ(%theta):
cis(-%theta/2), 0
0, cis(%theta/2)
## Controlled-NOT Variants
DEFGATE CNOT:
1, 0, 0, 0
0, 1, 0, 0
0, 0, 0, 1
0, 0, 1, 0
# Also known as the Toffoli gate.
DEFGATE CCNOT:
1, 0, 0, 0, 0, 0, 0, 0
0, 1, 0, 0, 0, 0, 0, 0
0, 0, 1, 0, 0, 0, 0, 0
0, 0, 0, 1, 0, 0, 0, 0
0, 0, 0, 0, 1, 0, 0, 0
0, 0, 0, 0, 0, 1, 0, 0
0, 0, 0, 0, 0, 0, 0, 1
0, 0, 0, 0, 0, 0, 1, 0
## Phase Gates
DEFGATE S:
1, 0
0, i
DEFGATE T:
1, 0
0, cis(pi/4)
DEFGATE PHASE(%alpha):
1, 0
0, cis(%alpha)
DEFGATE CPHASE00(%alpha):
cis(%alpha), 0, 0, 0
0, 1, 0, 0
0, 0, 1, 0
0, 0, 0, 1
DEFGATE CPHASE01(%alpha):
1, 0, 0, 0
0, cis(%alpha), 0, 0
0, 0, 1, 0
0, 0, 0, 1
DEFGATE CPHASE10(%alpha):
1, 0, 0, 0
0, 1, 0, 0
0, 0, cis(%alpha), 0
0, 0, 0, 1
DEFGATE CPHASE(%alpha):
1, 0, 0, 0
0, 1, 0, 0
0, 0, 1, 0
0, 0, 0, cis(%alpha)
DEFGATE CZ:
1, 0, 0, 0
0, 1, 0, 0
0, 0, 1, 0
0, 0, 0, -1
## Swap Gates
DEFGATE SWAP:
1, 0, 0, 0
0, 0, 1, 0
0, 1, 0, 0
0, 0, 0, 1
# Also known as the Fredkin gate.
DEFGATE CSWAP:
1, 0, 0, 0, 0, 0, 0, 0
0, 1, 0, 0, 0, 0, 0, 0
0, 0, 1, 0, 0, 0, 0, 0
0, 0, 0, 1, 0, 0, 0, 0
0, 0, 0, 0, 1, 0, 0, 0
0, 0, 0, 0, 0, 0, 1, 0
0, 0, 0, 0, 0, 1, 0, 0
0, 0, 0, 0, 0, 0, 0, 1
DEFGATE ISWAP:
1, 0, 0, 0
0, 0, i, 0
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
# 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