def cphase00_to_zz(gate: CPHASE00):
t = -gate.params['theta'] / (2 * np.pi)
q0, q1 = gate.qubits
circ = Circuit(
[X(0),
X(1),
ZZ(t, q0, q1),
TZ(-t, q0),
TZ(-t, q1),
X(0),
X(1)])
return circ
def cphase00_to_zz(gate: CPhase00):
t = -gate.param("theta") / (2 * pi)
q0, q1 = gate.qubits
circ = Circuit([
X(0),
X(1),
ZZ(t, q0, q1),
ZPow(-t, q0),
ZPow(-t, q1),
X(0),
X(1)
])
return circ
def identities():
""" Return a list of circuit identities, each consisting of a name, and
two equivalent Circuits."""
circuit_identities = []
# Pick random parameter
theta = np.pi * np.random.uniform()
# Single qubit gate identities
name = "Hadamard is own inverse"
circ0 = Circuit([H(0), H(0)])
circ1 = Circuit([I(0)])
circuit_identities.append([name, circ0, circ1])
name = "Hadamards convert X to Z"
circ0 = Circuit([H(0), X(0), H(0)])
circ1 = Circuit([Z(0)])
circuit_identities.append([name, circ0, circ1])
name = "Hadamards convert Z to X"
circ0 = Circuit([H(0), Z(0), H(0)])
circ1 = Circuit([X(0)])
circuit_identities.append([name, circ0, circ1])
name = "S sandwich converts X to Y"
circ0 = Circuit([S(0).H, X(0), S(0)])
circ1 = Circuit([Y(0)])
circuit_identities.append([name, circ0, circ1])
name = "S sandwich converts Y to X"
circ0 = Circuit([S(0), Y(0), S(0).H])
circ1 = Circuit([X(0)])
circuit_identities.append([name, circ0, circ1])
name = "Hadamards convert RZ to RX"
circ0 = Circuit([H(0), RZ(theta, 0), H(0)])
circ1 = Circuit([RX(theta, 0)])
circuit_identities.append([name, circ0, circ1])
# ZYZ Decompositions
name = "Hadamard ZYZ decomposition"
circ0 = Circuit([H(0)])
circ1 = Circuit([Z(0), Y(0)**0.5])
circuit_identities.append([name, circ0, circ1])
# CNOT identities
name = "CZ to CNOT"
circ0 = Circuit([CZ(0, 1)])
circ1 = Circuit([H(1), CNOT(0, 1), H(1)])
circuit_identities.append([name, circ0, circ1])
name = "SWAP to 3 CNOTs"
circ0 = Circuit([SWAP(0, 1)])
circ1 = Circuit([CNOT(0, 1), CNOT(1, 0), CNOT(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "SWAP to 3 CZs"
circ0 = Circuit([SWAP(0, 1)])
circ1 = Circuit(
[H(1),
CZ(0, 1),
H(0),
H(1),
CZ(1, 0),
H(0),
H(1),
CZ(0, 1),
H(1)])
circuit_identities.append([name, circ0, circ1])
name = "ISWAP decomposition to SWAP and CNOT"
circ0 = Circuit([ISWAP(0, 1)])
circ1 = Circuit([SWAP(0, 1), H(1), CNOT(0, 1), H(1), S(0), S(1)])
circuit_identities.append([name, circ0, circ1])
name = "ISWAP decomposition to SWAP and CZ"
# This makes it clear why you can commute RZ's across ISWAP
circ0 = Circuit([ISWAP(0, 1)])
circ1 = Circuit([SWAP(0, 1), CZ(0, 1), S(0), S(1)])
circuit_identities.append([name, circ0, circ1])
# http://info.phys.unm.edu/~caves/courses/qinfo-f14/lectures/lectures21-23.pdf
name = "CNOT sandwich with X on control"
circ0 = Circuit([CNOT(0, 1), X(0), CNOT(0, 1)])
circ1 = Circuit([X(0), X(1)])
circuit_identities.append([name, circ0, circ1])
# http://info.phys.unm.edu/~caves/courses/qinfo-f14/lectures/lectures21-23.pdf
name = "CNOT sandwich with Z on target"
circ0 = Circuit([CNOT(0, 1), Z(1), CNOT(0, 1)])
circ1 = Circuit([Z(0), Z(1)])
circuit_identities.append([name, circ0, circ1])
name = "DCNOT (Double-CNOT) to iSWAP"
circ0 = Circuit([CNOT(0, 1), CNOT(1, 0)])
circ1 = Circuit([H(0), S(0).H, S(1).H, ISWAP(0, 1), H(1)])
circuit_identities.append([name, circ0, circ1])
# Commuting single qubit gates across 2 qubit games
name = "Commute X on CNOT target"
circ0 = Circuit([X(1), CNOT(0, 1)])
circ1 = Circuit([CNOT(0, 1), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute X on CNOT control"
circ0 = Circuit([X(0), CNOT(0, 1)])
circ1 = Circuit([CNOT(0, 1), X(0), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Z on CNOT target"
circ0 = Circuit([Z(1), CNOT(0, 1)])
circ1 = Circuit([CNOT(0, 1), Z(0), Z(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Z on CNOT control"
circ0 = Circuit([Z(0), CNOT(0, 1)])
circ1 = Circuit([CNOT(0, 1), Z(0)])
circuit_identities.append([name, circ0, circ1])
# Canonical gate identities
name = "Canonical gates: CZ to ZZ"
circ0 = Circuit([CZ(0, 1), S(0), S(1)])
circ1 = Circuit([ZZ(0.5, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Canonical gates: XX to ZZ"
circ0 = Circuit([H(0), H(1), XX(0.5, 0, 1), H(0), H(1)])
circ1 = Circuit([ZZ(0.5, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Canonical gates: CNOT to XX"
circ0 = Circuit([CNOT(0, 1)])
circ1 = Circuit([H(0), XX(0.5, 0, 1), H(0), H(1), S(0).H, S(1).H, H(1)])
circuit_identities.append([name, circ0, circ1])
name = "Canonical gates: SWAP to Canonical"
circ0 = Circuit([SWAP(0, 1)])
circ1 = Circuit([CANONICAL(0.5, 0.5, 0.5, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "ISWAP to Canonical"
circ0 = Circuit([ISWAP(0, 1)])
circ1 = Circuit([CANONICAL(0.5, 0.5, 1.0, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "ISWAP to Canonical in Weyl chamber"
circ0 = Circuit([ISWAP(0, 1)])
circ1 = Circuit([X(0), CANONICAL(0.5, 0.5, 0.0, 0, 1), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "DCNOT to Canonical"
circ0 = Circuit([CNOT(0, 1), CNOT(1, 0)])
circ1 = Circuit([
H(0),
S(0).H,
S(1).H,
X(0),
CANONICAL(0.5, 0.5, 0.0, 0, 1),
X(1),
H(1)
])
circuit_identities.append([name, circ0, circ1])
# Multi-qubit circuits
name = "CNOT controls commute"
circ0 = Circuit([CNOT(1, 0), CNOT(1, 2)])
circ1 = Circuit([CNOT(1, 2), CNOT(1, 0)])
circuit_identities.append([name, circ0, circ1])
name = "CNOT targets commute"
circ0 = Circuit([CNOT(0, 1), CNOT(2, 1)])
circ1 = Circuit([CNOT(2, 1), CNOT(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Commutation of CNOT target/control"
circ0 = Circuit([CNOT(0, 1), CNOT(1, 2)])
circ1 = Circuit([CNOT(1, 2), CNOT(0, 2), CNOT(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Indirect CNOT and 4 CNOTS with intermediate qubit"
circ0 = Circuit([CNOT(0, 2), I(1)])
circ1 = Circuit([CNOT(0, 1), CNOT(1, 2), CNOT(0, 1), CNOT(1, 2)])
circuit_identities.append([name, circ0, circ1])
name = "CZs with shared shared qubit commute"
circ0 = Circuit([CZ(0, 1), CZ(1, 2)])
circ1 = Circuit([CZ(1, 2), CZ(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Toffoli gate CNOT decomposition"
circ0 = Circuit([CCNOT(0, 1, 2)])
circ1 = ccnot_circuit([0, 1, 2])
circuit_identities.append([name, circ0, circ1])
# Parametric circuits
name = "ZZ to CNOTs" # 1108.4318
circ0 = Circuit([ZZ(theta / np.pi, 0, 1)])
circ1 = Circuit([CNOT(0, 1), RZ(theta, 1), CNOT(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "XX to CNOTs" # 1108.4318
circ0 = Circuit([XX(theta / np.pi, 0, 1)])
circ1 = Circuit(
[H(0), H(1),
CNOT(0, 1),
RZ(theta, 1),
CNOT(0, 1),
H(0), H(1)])
circuit_identities.append([name, circ0, circ1])
name = "XX to CNOTs (2)"
circ0 = Circuit([XX(theta / np.pi, 0, 1)])
circ1 = Circuit([
Y(0)**0.5,
Y(1)**0.5,
CNOT(0, 1),
RZ(theta, 1),
CNOT(0, 1),
Y(0)**-0.5,
Y(1)**-0.5
])
circuit_identities.append([name, circ0, circ1])
name = "YY to CNOTs"
circ0 = Circuit([YY(theta / np.pi, 0, 1)])
circ1 = Circuit([
X(0)**0.5,
X(1)**0.5,
CNOT(0, 1),
RZ(theta, 1),
CNOT(0, 1),
X(0)**-0.5,
X(1)**-0.5
])
circuit_identities.append([name, circ0, circ1])
def cphase_to_zz(gate: CPHASE):
t = -gate.params['theta'] / (2 * np.pi)
q0, q1 = gate.qubits
circ = Circuit([ZZ(t, q0, q1), TZ(-t, q0), TZ(-t, q1)])
return circ
def cphase00_to_zz(gate: CPHASE00):
t = -gate.params['theta'] / (2 * np.pi)
q0, q1 = gate.qubits
circ = Circuit(
[X(0),
X(1),
ZZ(t, q0, q1),
TZ(-t, q0),
TZ(-t, q1),
X(0),
X(1)])
return circ
def cphase01_to_zz(gate: CPHASE00):
t = -gate.params['theta'] / (2 * np.pi)
q0, q1 = gate.qubits
circ = Circuit([X(0), ZZ(t, q0, q1), TZ(-t, q0), TZ(-t, q1), X(0)])
return circ
def cphase10_to_zz(gate: CPHASE00):
t = -gate.params['theta'] / (2 * np.pi)
q0, q1 = gate.qubits
circ = Circuit([X(1), ZZ(t, q0, q1), TZ(-t, q0), TZ(-t, q1), X(1)])
return circ
name = "CPHASE to ZZ"
gate = CPHASE(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "CPHASE00 to ZZ"
gate = CPHASE00(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase00_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "CPHASE01 to ZZ"
gate = CPHASE01(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase01_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "CPHASE10 to ZZ"
gate = CPHASE10(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase10_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
return circuit_identities
def identities():
"""Return a list of circuit identities, each consisting of a name, and
two equivalent Circuits."""
circuit_identities = []
# Pick random parameter
# theta = np.pi * np.random.uniform()
# t = np.random.uniform()
theta = syms["theta"]
t = syms["t"]
tx = syms["tx"]
ty = syms["ty"]
tz = syms["tz"]
# Single qubit gate identities
name = "Hadamard is own inverse"
circ0 = Circuit([H(0), H(0)])
circ1 = Circuit([I(0)])
circuit_identities.append([name, circ0, circ1])
name = "Hadamards convert X to Z"
circ0 = Circuit([H(0), X(0), H(0)])
circ1 = Circuit([Z(0)])
circuit_identities.append([name, circ0, circ1])
name = "Hadamards convert Z to X"
circ0 = Circuit([H(0), Z(0), H(0)])
circ1 = Circuit([X(0)])
circuit_identities.append([name, circ0, circ1])
name = "S sandwich converts X to Y"
circ0 = Circuit([S(0).H, X(0), S(0)])
circ1 = Circuit([Y(0)])
circuit_identities.append([name, circ0, circ1])
name = "S sandwich converts Y to X"
circ0 = Circuit([S(0), Y(0), S(0).H])
circ1 = Circuit([X(0)])
circuit_identities.append([name, circ0, circ1])
name = "Hadamards convert Rz to Rx"
circ0 = Circuit([H(0), Rz(theta, 0), H(0)])
circ1 = Circuit([Rx(theta, 0)])
circuit_identities.append([name, circ0, circ1])
# Simplified from Cirq's "_potential_cross_whole_w"
# "_potential_cross_partial_w" is essentially same identity
# X and ZPow commute
name = "X-sandwich inverts ZPow"
circ0 = Circuit([X(0), ZPow(t, 0), X(0)])
circ1 = Circuit([ZPow(-t, 0)])
circuit_identities.append([name, circ0, circ1])
# Same relation as previous
name = "Commute X past ZPow"
circ0 = Circuit([X(0), ZPow(t, 0)])
circ1 = Circuit([ZPow(-t, 0), X(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute X past YPow"
circ0 = Circuit([X(0), YPow(t, 0)])
circ1 = Circuit([YPow(-t, 0), X(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute V past ZPow"
circ0 = Circuit([V(0), ZPow(t, 0)])
circ1 = Circuit([YPow(t, 0), V(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute V past YPow"
circ0 = Circuit([V(0), YPow(t, 0)])
circ1 = Circuit([ZPow(-t, 0), V(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute V.H past ZPow"
circ0 = Circuit([V(0).H, ZPow(t, 0)])
circ1 = Circuit([YPow(-t, 0), V(0).H])
circuit_identities.append([name, circ0, circ1])
name = "Commute V.H past YPow"
circ0 = Circuit([V(0).H, YPow(t, 0)])
circ1 = Circuit([ZPow(t, 0), V(0).H])
circuit_identities.append([name, circ0, circ1])
name = "Couumte S.H past XPow"
circ0 = Circuit([S(0).H, XPow(t, 0)])
circ1 = Circuit([YPow(t, 0), S(0).H])
circuit_identities.append([name, circ0, circ1])
name = "Commute S past XPow"
circ0 = Circuit([S(0), XPow(t, 0)])
circ1 = Circuit([YPow(-t, 0), S(0)])
circuit_identities.append([name, circ0, circ1])
name = "Y to ZX"
circ0 = Circuit([Y(0)])
circ1 = Circuit([Z(0), X(0)])
circuit_identities.append([name, circ0, circ1])
# ZYZ Decompositions
name = "Hadamard ZYZ decomposition"
circ0 = Circuit([H(0)])
circ1 = Circuit([Z(0), Y(0)**0.5])
circuit_identities.append([name, circ0, circ1])
# CNot identities
name = "CZ to CNot"
circ0 = Circuit([CZ(0, 1)])
circ1 = Circuit([H(1), CNot(0, 1), H(1)])
circuit_identities.append([name, circ0, circ1])
name = "CZ to CNot (2)"
circ0 = Circuit([CZ(0, 1)])
circ1 = Circuit([YPow(+0.5, 1), CNot(0, 1), YPow(-0.5, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Swap to 3 CNots"
circ0 = Circuit([Swap(0, 1)])
circ1 = Circuit([CNot(0, 1), CNot(1, 0), CNot(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Swap to 3 CZs"
circ0 = Circuit([Swap(0, 1)])
circ1 = Circuit(
[CZ(0, 1),
H(0),
H(1),
CZ(1, 0),
H(0),
H(1),
CZ(0, 1),
H(0),
H(1)])
circuit_identities.append([name, circ0, circ1])
name = "ISwap decomposition to Swap and CNot"
circ0 = Circuit([ISwap(0, 1)])
circ1 = Circuit([Swap(0, 1), H(1), CNot(0, 1), H(1), S(0), S(1)])
circuit_identities.append([name, circ0, circ1])
name = "ISwap decomposition to Swap and CZ"
# This makes it clear why you can commute Rz's across ISwap
circ0 = Circuit([ISwap(0, 1)])
circ1 = Circuit([Swap(0, 1), CZ(0, 1), S(0), S(1)])
circuit_identities.append([name, circ0, circ1])
# http://info.phys.unm.edu/~caves/courses/qinfo-f14/lectures/lectures21-23.pdf
name = "CNot sandwich with X on control"
circ0 = Circuit([CNot(0, 1), X(0), CNot(0, 1)])
circ1 = Circuit([X(0), X(1)])
circuit_identities.append([name, circ0, circ1])
# http://info.phys.unm.edu/~caves/courses/qinfo-f14/lectures/lectures21-23.pdf
name = "CNot sandwich with Z on target"
circ0 = Circuit([CNot(0, 1), Z(1), CNot(0, 1)])
circ1 = Circuit([Z(0), Z(1)])
circuit_identities.append([name, circ0, circ1])
name = "DCNot (Double-CNot) to iSwap"
circ0 = Circuit([CNot(0, 1), CNot(1, 0)])
circ1 = Circuit([H(0), S(0).H, S(1).H, ISwap(0, 1), H(1)])
circuit_identities.append([name, circ0, circ1])
# Commuting single qubit gates across 2 qubit games
name = "Commute X on CNot target"
circ0 = Circuit([X(1), CNot(0, 1)])
circ1 = Circuit([CNot(0, 1), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute X on CNot control"
circ0 = Circuit([X(0), CNot(0, 1)])
circ1 = Circuit([CNot(0, 1), X(0), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Z on CNot target"
circ0 = Circuit([Z(1), CNot(0, 1)])
circ1 = Circuit([CNot(0, 1), Z(0), Z(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Z on CNot control"
circ0 = Circuit([Z(0), CNot(0, 1)])
circ1 = Circuit([CNot(0, 1), Z(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute X with CZ"
circ0 = Circuit([X(0), CZ(0, 1)])
circ1 = Circuit([CZ(0, 1), X(0), Z(1)])
circuit_identities.append([name, circ0, circ1])
name = "Commute X with XX"
circ0 = Circuit([X(0), XX(t, 0, 1)])
circ1 = Circuit([
XX(t, 0, 1),
X(0),
])
circuit_identities.append([name, circ0, circ1])
name = "Commute X with YY"
circ0 = Circuit([X(0), YY(t, 0, 1)])
circ1 = Circuit([
YY(-t, 0, 1),
X(0),
])
circuit_identities.append([name, circ0, circ1])
name = "Commute X with ZZ"
circ0 = Circuit([X(0), ZZ(t, 0, 1)])
circ1 = Circuit([
ZZ(-t, 0, 1),
X(0),
])
circuit_identities.append([name, circ0, circ1])
name = "Commute X with Canonical"
circ0 = Circuit([X(0), Can(tx, ty, tz, 0, 1)])
circ1 = Circuit([Can(tx, -ty, -tz, 0, 1), X(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Y with Canonical"
circ0 = Circuit([Y(0), Can(tx, ty, tz, 0, 1)])
circ1 = Circuit([Can(-tx, ty, -tz, 0, 1), Y(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Z with Canonical"
circ0 = Circuit([Z(0), Can(tx, ty, tz, 0, 1)])
circ1 = Circuit([Can(-tx, -ty, tz, 0, 1), Z(0)])
circuit_identities.append([name, circ0, circ1])
name = "Commute Sqrt(X) with Canonical switches ty and tz arguments"
circ0 = Circuit([V(0), V(1), Can(tx, ty, tz, 0, 1)])
circ1 = Circuit([Can(tx, tz, ty, 0, 1), V(0), V(1)])
circuit_identities.append([name, circ0, circ1])
# Canonical decompositions
name = "Canonical gates: CZ to ZZ"
circ0 = Circuit([CZ(0, 1), S(0), S(1)])
circ1 = Circuit([ZZ(0.5, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Canonical gates: XX to ZZ"
circ0 = Circuit([H(0), H(1), XX(0.5, 0, 1), H(0), H(1)])
circ1 = Circuit([ZZ(0.5, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Canonical gates: CNot to XX"
circ0 = Circuit([CNot(0, 1)])
circ1 = Circuit([H(0), XX(0.5, 0, 1), H(0), H(1), S(0).H, S(1).H, H(1)])
circuit_identities.append([name, circ0, circ1])
name = "Canonical gates: Swap to Canonical"
circ0 = Circuit([Swap(0, 1)])
circ1 = Circuit([Can(0.5, 0.5, 0.5, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "ISwap to Canonical"
circ0 = Circuit([ISwap(0, 1)])
circ1 = Circuit([Can(-0.5, -0.5, 0.0, 0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "ISwap to Canonical in Weyl chamber"
circ0 = Circuit([ISwap(0, 1)])
circ1 = Circuit([X(0), Can(0.5, 0.5, 0.0, 0, 1), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "ISwap conjugate to ISwap"
circ0 = Circuit([ISwap(0, 1).H])
circ1 = Circuit([X(0), ISwap(0, 1), X(1)])
circuit_identities.append([name, circ0, circ1])
name = "DCNot to Canonical"
circ0 = Circuit([CNot(0, 1), CNot(1, 0)])
circ1 = Circuit(
[H(0),
S(0).H,
S(1).H,
X(0),
Can(0.5, 0.5, 0.0, 0, 1),
X(1),
H(1)])
circuit_identities.append([name, circ0, circ1])
# Multi-qubit circuits
name = "CNot controls commute"
circ0 = Circuit([CNot(1, 0), CNot(1, 2)])
circ1 = Circuit([CNot(1, 2), CNot(1, 0)])
circuit_identities.append([name, circ0, circ1])
name = "CNot targets commute"
circ0 = Circuit([CNot(0, 1), CNot(2, 1)])
circ1 = Circuit([CNot(2, 1), CNot(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Commutation of CNot target/control"
circ0 = Circuit([CNot(0, 1), CNot(1, 2)])
circ1 = Circuit([CNot(1, 2), CNot(0, 2), CNot(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Indirect CNot and 4 CNotS with intermediate qubit"
circ0 = Circuit([CNot(0, 2), I(1)])
circ1 = Circuit([CNot(0, 1), CNot(1, 2), CNot(0, 1), CNot(1, 2)])
circuit_identities.append([name, circ0, circ1])
name = "CZs with shared shared qubit commute"
circ0 = Circuit([CZ(0, 1), CZ(1, 2)])
circ1 = Circuit([CZ(1, 2), CZ(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "Z's shift ZZ by one unit"
circ0 = Circuit([ZZ(t, 0, 1)])
circ1 = Circuit([ZZ(t + 1, 0, 1), Z(0), Z(1)])
circuit_identities.append([name, circ0, circ1])
name = "Z's shift ZZ by one unit"
circ0 = Circuit([XX(t, 0, 1)])
circ1 = Circuit([XX(t + 1, 0, 1), X(0), X(1)])
circuit_identities.append([name, circ0, circ1])
# Parametric circuits
name = "ZZ to CNots" # 1108.4318
circ0 = Circuit([ZZ(theta / pi, 0, 1)])
circ1 = Circuit([CNot(0, 1), Rz(theta, 1), CNot(0, 1)])
circuit_identities.append([name, circ0, circ1])
name = "XX to CNots" # 1108.4318
circ0 = Circuit([XX(theta / pi, 0, 1)])
circ1 = Circuit(
[H(0), H(1),
CNot(0, 1),
Rz(theta, 1),
CNot(0, 1),
H(0), H(1)])
circuit_identities.append([name, circ0, circ1])
name = "XX to CNots (2)"
circ0 = Circuit([XX(theta / pi, 0, 1)])
circ1 = Circuit([
Y(0)**0.5,
Y(1)**0.5,
CNot(0, 1),
Rz(theta, 1),
CNot(0, 1),
Y(0)**-0.5,
Y(1)**-0.5,
])
circuit_identities.append([name, circ0, circ1])
name = "YY to CNots"
circ0 = Circuit([YY(theta / pi, 0, 1)])
circ1 = Circuit([
X(0)**0.5,
X(1)**0.5,
CNot(0, 1),
Rz(theta, 1),
CNot(0, 1),
X(0)**-0.5,
X(1)**-0.5,
])
circuit_identities.append([name, circ0, circ1])
def cphase_to_zz(gate: CPhase):
t = -gate.param("theta") / (2 * pi)
q0, q1 = gate.qubits
circ = Circuit([ZZ(t, q0, q1), ZPow(-t, q0), ZPow(-t, q1)])
return circ
def cphase00_to_zz(gate: CPhase00):
t = -gate.param("theta") / (2 * pi)
q0, q1 = gate.qubits
circ = Circuit([
X(0),
X(1),
ZZ(t, q0, q1),
ZPow(-t, q0),
ZPow(-t, q1),
X(0),
X(1)
])
return circ
def cphase01_to_zz(gate: CPhase00):
t = -gate.param("theta") / (2 * pi)
q0, q1 = gate.qubits
circ = Circuit([X(0), ZZ(t, q0, q1), ZPow(-t, q0), ZPow(-t, q1), X(0)])
return circ
def cphase10_to_zz(gate: CPhase00):
t = -gate.param("theta") / (2 * pi)
q0, q1 = gate.qubits
circ = Circuit([X(1), ZZ(t, q0, q1), ZPow(-t, q0), ZPow(-t, q1), X(1)])
return circ
name = "CPhase to ZZ"
gate = CPhase(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "CPhase00 to ZZ"
gate = CPhase00(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase00_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "CPhase01 to ZZ"
gate = CPhase01(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase01_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "CPhase10 to ZZ"
gate = CPhase10(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = cphase10_to_zz(gate)
circuit_identities.append([name, circ0, circ1])
name = "PSwap to Canonical"
gate = PSwap(theta, 0, 1)
circ0 = Circuit([gate])
circ1 = Circuit()
circ1 += YPow(1, 0)
circ1 += Can(0.5, 0.5, 0.5 - theta / pi, 0, 1)
circ1 += YPow(1, 1)
circuit_identities.append([name, circ0, circ1])
# Three qubit gates
name = "Toffoli gate CNot decomposition"
circ0 = Circuit([CCNot(0, 1, 2)])
circ1 = translate_ccnot_to_cnot(CCNot(0, 1, 2))
circuit_identities.append([name, circ0, circ1])
name = "CCZ to CNots, respecting adjacency"
gate = CCZ(0, 1, 2)
circ0 = Circuit([gate])
circ1 = Circuit(translate_ccz_to_adjacent_cnot(gate))
circuit_identities.append([name, circ0, circ1])
name = "CCNot to CCZ"
gate = CCNot(0, 1, 2)
circ0 = Circuit([gate])
circ1 = Circuit(translate_ccnot_to_ccz(gate))
circuit_identities.append([name, circ0, circ1])
name = "CSwap to CCNot"
gate = CSwap(0, 1, 2)
circ0 = Circuit([gate])
circ1 = Circuit(translate_cswap_to_ccnot(gate))
circuit_identities.append([name, circ0, circ1])
name = "CSwap to CNot"
gate = CSwap(0, 1, 2)
circ0 = Circuit([gate])
circ1 = Circuit(translate_cswap_to_cnot(gate))
circuit_identities.append([name, circ0, circ1])
name = "CSwap to CNot (control between targets)"
gate = CSwap(1, 0, 2)
circ0 = Circuit([gate])
circ1 = Circuit(translate_cswap_inside_to_cnot(gate))
circuit_identities.append([name, circ0, circ1])
name = "CH to Clifford+T"
gate = CH(0, 1)
circ0 = Circuit([gate])
circ1 = Circuit(translate_ch_to_cpt(gate))
circuit_identities.append([name, circ0, circ1])
name = "CV to Clifford+T"
gate = CV(0, 1)
circ0 = Circuit([gate])
circ1 = Circuit(translate_cv_to_cpt(gate))
circuit_identities.append([name, circ0, circ1])
name = "CV_H to Clifford+T"
gate = CV_H(0, 1)
circ0 = Circuit([gate])
circ1 = Circuit(translate_cvh_to_cpt(gate))
circuit_identities.append([name, circ0, circ1])
# from sympy import Symbol, pi
name = "CNotPow to ZZ"
gate = CNotPow(t, 0, 1)
circ0 = Circuit([gate])
circ1 = Circuit(translate_cnotpow_to_zz(gate))
circuit_identities.append([name, circ0, circ1])
# name = "PISwap to XY"
# gate = PISwap(theta, 0, 1)
# circ0 = Circuit([gate])
# circ1 = Circuit(translate_piswap_to_xy(gate))
# circuit_identities.append([name, circ0, circ1])
name = "Powers of iSwap to CNot sandwich"
gate = ISwap(0, 1)**t
trans = [translate_xy_to_can, translate_can_to_cnot]
circ0 = Circuit([gate])
circ1 = circuit_translate(circ0, trans)
circuit_identities.append([name, circ0, circ1])
name = "Commute ZPow past multiple CNots"
gate = ZPow(t, 1)
circ0 = Circuit([gate, CNot(0, 1), CNot(1, 2), CNot(0, 1)])
circ1 = Circuit([CNot(0, 1), CNot(1, 2), CNot(0, 1), gate])
circuit_identities.append([name, circ0, circ1])
return circuit_identities