def double_exchange(angle,
qubit_pair_1,
qubit_pair_2,
parity_dependence=False,
d_exc_correction=False):
assert len(qubit_pair_1) == 2
assert len(qubit_pair_2) == 2
theta_1 = numpy.pi / 2 - angle
qasm = ['']
# 1st exchange + 0-2
qasm.append(QasmUtils.controlled_xz(qubit_pair_2[0], qubit_pair_1[0]))
qasm.append('ry({}) q[{}];\n'.format(theta_1, qubit_pair_2[0]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_2[0]))
qasm.append('ry({}) q[{}];\n'.format(-theta_1, qubit_pair_2[0]))
# 2nd exchange + 1-3
qasm.append(QasmUtils.controlled_xz(qubit_pair_2[1], qubit_pair_1[1]))
qasm.append('ry({}) q[{}];\n'.format(theta_1, qubit_pair_2[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[1],
qubit_pair_2[1]))
qasm.append('ry({}) q[{}];\n'.format(-theta_1, qubit_pair_2[1]))
# CZ gates
qasm.append('cz q[{}], q[{}];\n'.format(qubit_pair_2[0],
qubit_pair_2[1]))
# qasm.append('cz q[{}], q[{}];\n'.format(qubit_pair_1[0], qubit_pair_1[1]))
# correction 3rd order terms approximates the operation of a double exchange
if d_exc_correction:
angle_2 = DoubleExchange.second_angle(angle)
# not correcting 3rd order terms approximates the operation of a double excitation (with 3rd order error terms)
else:
angle_2 = angle
theta_2 = numpy.pi / 2 - angle_2
# 3rd exchange - 0-2
qasm.append('ry({}) q[{}];\n'.format(theta_2, qubit_pair_2[0]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_2[0]))
qasm.append('ry({}) q[{}];\n'.format(-theta_2, qubit_pair_2[0]))
qasm.append(
QasmUtils.controlled_xz(qubit_pair_2[0],
qubit_pair_1[0],
reverse=True))
# 4th exchange -1-3
qasm.append('ry({}) q[{}];\n'.format(theta_2, qubit_pair_2[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[1],
qubit_pair_2[1]))
qasm.append('ry({}) q[{}];\n'.format(-theta_2, qubit_pair_2[1]))
qasm.append(
QasmUtils.controlled_xz(qubit_pair_2[1],
qubit_pair_1[1],
reverse=True))
# correcting for parameter sign
if parity_dependence:
# do not include the first qubit of the second pair
parity_qubits = list(range(
min(qubit_pair_1), max(qubit_pair_1))) + list(
range(min(qubit_pair_2) + 1, max(qubit_pair_2)))
# ladder of CNOT used to determine the parity
cnot_ladder = ['']
for i in range(len(parity_qubits) - 1):
cnot_ladder.append('cx q[{}], q[{}];\n'.format(
parity_qubits[i], parity_qubits[i + 1]))
if angle > 0:
# applies a CZ correction in front, to get a negative sign for the excitation term, if the parity is 1
# (or the parity of "parity_qubits" is 0)
front = ['']
# this is the CZ that determines the sign of the excitation term
front.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
# this bit determines the parity and applies a CZ to negate the correction if the parity is wrong
front += cnot_ladder
front.append('x q[{}];\n'.format(parity_qubits[-1]))
front.append('cz q[{}], q[{}];\n'.format(
parity_qubits[-1], qubit_pair_2[0]))
front.append('x q[{}];\n'.format(parity_qubits[-1]))
front += cnot_ladder[::-1]
# .. positive sign for the excitation term, if the parity is 0 (or the parity of "parity_qubits" is 1)
rear = ['']
# .. sign correction
rear.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
# .. parity correction
rear += cnot_ladder
rear.append('cz q[{}], q[{}];\n'.format(
parity_qubits[-1], qubit_pair_2[0]))
rear += cnot_ladder[::-1]
# additional correction of states 010 and 110
rear.append('x q[{}];\n'.format(qubit_pair_2[1]))
rear.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
rear.append('x q[{}];\n'.format(qubit_pair_2[1]))
qasm = front + qasm + rear
else:
front = ['']
# sign correction
front.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
# parity correction
front += cnot_ladder
front.append('cz q[{}], q[{}];\n'.format(
parity_qubits[-1], qubit_pair_2[0]))
front += cnot_ladder[::-1]
rear = ['']
# sign correction
rear.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
# parity correction
rear += cnot_ladder
rear.append('x q[{}];\n'.format(parity_qubits[-1]))
rear.append('cz q[{}], q[{}];\n'.format(
parity_qubits[-1], qubit_pair_2[0]))
rear.append('x q[{}];\n'.format(parity_qubits[-1]))
rear += cnot_ladder[::-1]
# 010 and 011 correction
rear.append('x q[{}];\n'.format(qubit_pair_2[1]))
rear.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
rear.append('x q[{}];\n'.format(qubit_pair_2[1]))
qasm = front + qasm + rear
else:
if angle > 0:
# adding a correcting CZ gate at the end will result in a minus sign
qasm.append('cz q[{}], q[{}];\n'.format(
qubit_pair_2[0], qubit_pair_2[1]))
# qasm.append('cz q[{}], q[{}];\n'.format(qubit_pair_1[0], qubit_pair_1[1]))
else:
# adding a correcting CZ gate at the front will result in a plus sign
qasm = ['cz q[{}], q[{}];\n'.format(qubit_pair_2[0], qubit_pair_2[1]),
] \
+ qasm
# 'cz q[{}], q[{}];\n'.format(qubit_pair_1[0], qubit_pair_1[1])
return ''.join(qasm)
def efficient_double_excitation_2(angle, qubit_pair_1, qubit_pair_2):
qasm = ['']
theta = angle / 8
# determine the parity of the two pairs
qasm.append('cx q[{}], q[{}];\n'.format(*qubit_pair_1))
qasm.append('x q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('cx q[{}], q[{}];\n'.format(*qubit_pair_2))
qasm.append('x q[{}];\n'.format(qubit_pair_2[1]))
# apply a partial swap of qubits 0 and 2, controlled by 1 and 3 ##
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_2[0]))
# # partial ccc_y operation
qasm.append('rz({}) q[{}];\n'.format(numpy.pi / 2, qubit_pair_1[0]))
qasm.append('rx({}) q[{}];\n'.format(theta, qubit_pair_1[0])) # +
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_1[1])) # 0 1
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('rx({}) q[{}];\n'.format(-theta, qubit_pair_1[0])) # -
qasm.append('h q[{}];\n'.format(qubit_pair_2[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_2[1])) # 0 3
qasm.append('h q[{}];\n'.format(qubit_pair_2[1]))
qasm.append('rx({}) q[{}];\n'.format(theta, qubit_pair_1[0])) # +
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_1[1])) # 0 1
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('rx({}) q[{}];\n'.format(-theta, qubit_pair_1[0])) # -
qasm.append('h q[{}];\n'.format(qubit_pair_2[0]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_2[0])) # 0 2
qasm.append('h q[{}];\n'.format(qubit_pair_2[0]))
qasm.append('rx({}) q[{}];\n'.format(theta, qubit_pair_1[0])) # +
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_1[1])) # 0 1
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('rx({}) q[{}];\n'.format(-theta, qubit_pair_1[0])) # -
qasm.append('h q[{}];\n'.format(qubit_pair_2[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_2[1])) # 0 3
qasm.append('h q[{}];\n'.format(qubit_pair_2[1]))
qasm.append('rx({}) q[{}];\n'.format(theta, qubit_pair_1[0])) # +
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0],
qubit_pair_1[1])) # 0 1
qasm.append('h q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('rx({}) q[{}];\n'.format(-theta, qubit_pair_1[0])) # -
qasm.append('rz({}) q[{}];\n'.format(-numpy.pi / 2, qubit_pair_1[0]))
##### test #####
# qasm.append('h q[{}];\n'.format(qubit_pair_2[0]))
# qasm.append('cx q[{}], q[{}];\n'.format(qubit_pair_1[0], qubit_pair_2[0])) # 0 2
# qasm.append('h q[{}];\n'.format(qubit_pair_2[0]))
# ###############
# partial ccc_y operation ############ to here
qasm.append(
QasmUtils.controlled_xz(qubit_pair_1[0],
qubit_pair_2[0],
reverse=True))
# correct for parity determination
qasm.append('x q[{}];\n'.format(qubit_pair_1[1]))
qasm.append('cx q[{}], q[{}];\n'.format(*qubit_pair_1))
qasm.append('x q[{}];\n'.format(qubit_pair_2[1]))
qasm.append('cx q[{}], q[{}];\n'.format(*qubit_pair_2))
return ''.join(qasm)