def _set_row_x_zero(clifford, circuit, qubit):
"""Set destabilizer.X[qubit, i] to False for all i > qubit.
This is done by applying CNOTS assumes k<=N and A[k][k]=1
"""
x = clifford.destabilizer.X[qubit]
z = clifford.destabilizer.Z[qubit]
# Check X first
for i in range(qubit + 1, clifford.num_qubits):
if x[i]:
_append_cx(clifford, qubit, i)
circuit.cx(qubit, i)
# Check whether Zs need to be set to zero:
if np.any(z[qubit:]):
if not z[qubit]:
# to treat Zs: make sure row.Z[k] to True
_append_s(clifford, qubit)
circuit.s(qubit)
# reverse CNOTS
for i in range(qubit + 1, clifford.num_qubits):
if z[i]:
_append_cx(clifford, i, qubit)
circuit.cx(i, qubit)
# set row.Z[qubit] to False
_append_s(clifford, qubit)
circuit.s(qubit)
def _set_row_z_zero(clifford, circuit, qubit):
"""Set stabilizer.Z[qubit, i] to False for all i > qubit.
Implemented by applying (reverse) CNOTS assumes qubit < num_qubits
and _set_row_x_zero has been called first
"""
x = clifford.stabilizer.X[qubit]
z = clifford.stabilizer.Z[qubit]
# check whether Zs need to be set to zero:
if np.any(z[qubit + 1:]):
for i in range(qubit + 1, clifford.num_qubits):
if z[i]:
_append_cx(clifford, i, qubit)
circuit.cx(i, qubit)
# check whether Xs need to be set to zero:
if np.any(x[qubit:]):
_append_h(clifford, qubit)
circuit.h(qubit)
for i in range(qubit + 1, clifford.num_qubits):
if x[i]:
_append_cx(clifford, qubit, i)
circuit.cx(qubit, i)
if z[qubit]:
_append_s(clifford, qubit)
circuit.s(qubit)
_append_h(clifford, qubit)
circuit.h(qubit)
def _reduce_cost(clifford, inv_circuit, cost):
"""Two-qubit cost reduction step"""
num_qubits = clifford.num_qubits
for qubit0 in range(num_qubits):
for qubit1 in range(qubit0 + 1, num_qubits):
for n0, n1 in product(range(3), repeat=2):
# Apply a 2-qubit block
reduced = clifford.copy()
for qubit, n in [(qubit0, n0), (qubit1, n1)]:
if n == 1:
_append_v(reduced, qubit)
elif n == 2:
_append_w(reduced, qubit)
_append_cx(reduced, qubit0, qubit1)
# Compute new cost
new_cost = _cx_cost(reduced)
if new_cost == cost - 1:
# Add decomposition to inverse circuit
for qubit, n in [(qubit0, n0), (qubit1, n1)]:
if n == 1:
inv_circuit.sdg(qubit)
inv_circuit.h(qubit)
elif n == 2:
inv_circuit.h(qubit)
inv_circuit.s(qubit)
inv_circuit.cx(qubit0, qubit1)
return reduced, inv_circuit, new_cost
# If we didn't reduce cost
raise QiskitError("Failed to reduce Clifford CX cost.")
def _calc_decoupling(cliff_ox, cliff_oz, qubit_list, min_qubit, num_qubits):
"""Calculate a decoupling operator D:
D^{-1} * Ox * D = x1
D^{-1} * Oz * D = z1
and reduce the clifford such that it will act trivially on min_qubit
"""
circ = QuantumCircuit(num_qubits)
# decouple_cliff is initialized to an identity clifford
decouple_cliff = cliff_ox.copy()
num_qubits = decouple_cliff.num_qubits
decouple_cliff.table.phase = np.zeros(2 * num_qubits)
if (decouple_cliff.table.array != np.eye(2 * num_qubits)).any():
raise QiskitError("Symplectic Gaussian elimination fails.")
qubit0 = min_qubit # The qubit for the symplectic Gaussian elimination
# Reduce the pair of Paulis to a representative in the equivalence class
# ['XZ', 'XX', 'XI', 'IZ', 'II'] by adding single-qubit gates
for qubit in qubit_list:
typeq = _from_pair_cliffs_to_type(cliff_ox, cliff_oz, qubit)
if typeq in [
[[True, True], [False, False]], # 'YI'
[[True, True], [True, True]], # 'YY'
[[True, True], [True, False]]
]: # 'YZ':
circ.s(qubit)
_append_s(decouple_cliff, qubit)
elif typeq in [
[[True, False], [False, False]], # 'ZI'
[[True, False], [True, False]], # 'ZZ'
[[True, False], [False, True]], # 'ZX'
[[False, False], [False, True]]
]: # 'IX'
circ.h(qubit)
_append_h(decouple_cliff, qubit)
elif typeq in [
[[False, False], [True, True]], # 'IY'
[[True, False], [True, True]]
]: # 'ZY'
circ.s(qubit)
circ.h(qubit)
_append_s(decouple_cliff, qubit)
_append_h(decouple_cliff, qubit)
elif typeq == [[True, True], [False, True]]: # 'YX'
circ.h(qubit)
circ.s(qubit)
_append_h(decouple_cliff, qubit)
_append_s(decouple_cliff, qubit)
elif typeq == [[False, True], [True, True]]: # 'XY'
circ.s(qubit)
circ.h(qubit)
circ.s(qubit)
_append_s(decouple_cliff, qubit)
_append_h(decouple_cliff, qubit)
_append_s(decouple_cliff, qubit)
# Reducing each pair of Paulis (except of qubit0) to 'II'
# by adding two-qubit gates and single-qubit gates
A_qubits = []
B_qubits = []
C_qubits = []
D_qubits = []
for qubit in qubit_list:
typeq = _from_pair_cliffs_to_type(cliff_ox, cliff_oz, qubit)
if typeq in A_class:
A_qubits.append(qubit)
elif typeq in B_class:
B_qubits.append(qubit)
elif typeq in C_class:
C_qubits.append(qubit)
elif typeq in D_class:
D_qubits.append(qubit)
if len(A_qubits) % 2 != 1:
raise QiskitError("Symplectic Gaussian elimination fails.")
if qubit0 not in A_qubits: # SWAP qubit0 and qubitA
qubitA = A_qubits[0]
circ.swap(qubit0, qubitA)
_append_swap(decouple_cliff, qubit0, qubitA)
if qubit0 in B_qubits:
B_qubits.remove(qubit0)
B_qubits.append(qubitA)
A_qubits.remove(qubitA)
A_qubits.append(qubit0)
elif qubit0 in C_qubits:
C_qubits.remove(qubit0)
C_qubits.append(qubitA)
A_qubits.remove(qubitA)
A_qubits.append(qubit0)
elif qubit0 in D_qubits:
D_qubits.remove(qubit0)
D_qubits.append(qubitA)
A_qubits.remove(qubitA)
A_qubits.append(qubit0)
else:
A_qubits.remove(qubitA)
A_qubits.append(qubit0)
# Reduce pairs in Class C to 'II'
for qubit in C_qubits:
circ.cx(qubit0, qubit)
_append_cx(decouple_cliff, qubit0, qubit)
# Reduce pairs in Class D to 'II'
for qubit in D_qubits:
circ.cx(qubit, qubit0)
_append_cx(decouple_cliff, qubit, qubit0)
# Reduce pairs in Class B to 'II'
if len(B_qubits) > 1:
for qubit in B_qubits[1:]:
qubitB = B_qubits[0]
circ.cx(qubitB, qubit)
_append_cx(decouple_cliff, qubitB, qubit)
if len(B_qubits) > 0:
qubitB = B_qubits[0]
circ.cx(qubit0, qubitB)
circ.h(qubitB)
circ.cx(qubitB, qubit0)
_append_cx(decouple_cliff, qubit0, qubitB)
_append_h(decouple_cliff, qubitB)
_append_cx(decouple_cliff, qubitB, qubit0)
# Reduce pairs in Class A (except of qubit0) to 'II'
Alen = int((len(A_qubits) - 1) / 2)
if Alen > 0:
A_qubits.remove(qubit0)
for qubit in range(Alen):
circ.cx(A_qubits[2 * qubit + 1], A_qubits[2 * qubit])
circ.cx(A_qubits[2 * qubit], qubit0)
circ.cx(qubit0, A_qubits[2 * qubit + 1])
_append_cx(decouple_cliff, A_qubits[2 * qubit + 1],
A_qubits[2 * qubit])
_append_cx(decouple_cliff, A_qubits[2 * qubit], qubit0)
_append_cx(decouple_cliff, qubit0, A_qubits[2 * qubit + 1])
return circ, decouple_cliff
