def time_evolution_circuit_improved(g_list,
t,
kickback_phase,
k,
n_trotter_step=1):
n_qubits = 3
a_idx = 2
phi = -(t / n_trotter_step) * g_list
# print(phi)
circuit = QuantumCircuit(n_qubits)
circuit.add_H_gate(a_idx)
# Apply kickback phase rotation to ancilla bit
circuit.add_RZ_gate(a_idx, -np.pi * kickback_phase / 2)
for _ in range(n_trotter_step):
for _ in range(2**k):
# CU(Z0)
circuit.add_RZ_gate(0, -phi[0])
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_RZ_gate(0, phi[0])
circuit.add_CNOT_gate(a_idx, 0)
# CU(Y0 Y1)
circuit.add_S_gate(0)
circuit.add_S_gate(1)
circuit.add_H_gate(0)
circuit.add_H_gate(1)
circuit.add_CNOT_gate(1, 0)
circuit.add_RZ_gate(0, -phi[1])
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_RZ_gate(0, phi[1])
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_CNOT_gate(1, 0)
circuit.add_H_gate(0)
circuit.add_H_gate(1)
circuit.add_Sdag_gate(0)
circuit.add_Sdag_gate(1)
# CU(Z1)
circuit.add_RZ_gate(1, -phi[2])
circuit.add_CNOT_gate(a_idx, 1)
circuit.add_RZ_gate(1, phi[2])
circuit.add_CNOT_gate(a_idx, 1)
# CU(X0 X1)
circuit.add_H_gate(0)
circuit.add_H_gate(1)
circuit.add_CNOT_gate(1, 0)
circuit.add_RZ_gate(0, -phi[3])
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_RZ_gate(0, phi[3])
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_CNOT_gate(1, 0)
circuit.add_H_gate(0)
circuit.add_H_gate(1)
circuit.add_H_gate(a_idx)
return circuit
def test_CU_Y0Y1(self):
n_qubits = 3
a_idx = 2
theta = np.pi/4
state = QuantumState(n_qubits)
input_states_bin = [0b001, 0b010, 0b101, 0b110]
input_states = []
output_states = []
circuit = QuantumCircuit(n_qubits)
# change basis from Z to Y
circuit.add_S_gate(0)
circuit.add_S_gate(1)
circuit.add_H_gate(0)
circuit.add_H_gate(1)
circuit.add_CNOT_gate(1, 0)
# RZ
circuit.add_RZ_gate(0, -0.5*theta)
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_RZ_gate(0, 0.5*theta)
circuit.add_CNOT_gate(a_idx, 0)
circuit.add_CNOT_gate(1, 0)
# change basis from Z to Y
circuit.add_H_gate(0)
circuit.add_H_gate(1)
circuit.add_Sdag_gate(0)
circuit.add_Sdag_gate(1)
for b in input_states_bin:
psi = state.copy()
psi.set_computational_basis(b)
input_states += [psi]
psi_out = psi.copy()
circuit.update_quantum_state(psi_out)
output_states += [psi_out]
p_list = []
for in_state in input_states:
for out_state in output_states:
prod = inner_product(in_state, out_state)
p_list += [prod]
# |001>
exp_list = [1.0, 0.0, 0.0, 0.0]
# |010>
exp_list += [0.0, 1.0, 0.0, 0.0]
# |101>
exp_list += [0.0, 0.0, np.cos(theta/2), complex(0, -np.sin(theta/2))]
# |110>
exp_list += [0.0, 0.0, complex(0, -np.sin(theta/2)), np.cos(theta/2)]
for result, expected in zip(p_list, exp_list):
self.assertAlmostEqual(result, expected, places=6)
def sample_observable_noisy_circuit(circuit,
initial_state,
obs,
n_circuit_sample=1000,
n_sample_per_circuit=1):
"""
Args:
circuit (:class:`qulacs.QuantumCircuit`)
initial_state (:class:`qulacs.QuantumState`)
obs (:class:`qulacs.Observable`)
n_circuit_sample (:class:`int`): number of circuit samples
n_sample (:class:`int`): number of samples per one circuit samples
Return:
:float: sampled expectation value of the observable
"""
n_term = obs.get_term_count()
n_qubit = obs.get_qubit_count()
pauli_terms = [obs.get_term(i) for i in range(n_term)]
coefs = [p.get_coef() for p in pauli_terms]
pauli_ids = [p.get_pauli_id_list() for p in pauli_terms]
pauli_indices = [p.get_index_list() for p in pauli_terms]
exp = 0
state = initial_state.copy()
for c in range(n_circuit_sample):
state.load(initial_state)
circuit.update_quantum_state(state)
for i in range(n_term):
measurement_circuit = QuantumCircuit(n_qubit)
if len(pauli_ids[i]) == 0: # means identity
exp += coefs[i]
continue
mask = ''.join([
'1' if n_qubit - 1 - k in pauli_indices[i] else '0'
for k in range(n_qubit)
])
for single_pauli, index in zip(pauli_ids[i], pauli_indices[i]):
if single_pauli == 1:
measurement_circuit.add_H_gate(index)
elif single_pauli == 2:
measurement_circuit.add_Sdag_gate(index)
uncompute_circuit.add_H_gate(index)
measurement_circuit.update_quantum_state(state)
samples = state.sampling(n_sample_per_circuit)
mask = int(mask, 2)
exp += coefs[i] * sum(
list(map(lambda x: (-1)**(bin(x & mask).count('1')),
samples))) / n_sample_per_circuit
exp /= n_circuit_sample
return exp
def sample_observable(state, obs, n_sample):
"""Function
Args:
state (qulacs.QuantumState):
obs (qulacs.Observable)
n_sample (int): number of samples for each observable
Return:
:float: sampled expectation value of the observable
Author(s): Takashi Tsuchimochi
"""
n_term = obs.get_term_count()
n_qubits = obs.get_qubit_count()
exp = 0
buf_state = QuantumState(n_qubits)
for i in range(n_term):
pauli_term = obs.get_term(i)
coef = pauli_term.get_coef()
pauli_id = pauli_term.get_pauli_id_list()
pauli_index = pauli_term.get_index_list()
if len(pauli_id) == 0: # means identity
exp += coef
continue
buf_state.load(state)
measurement_circuit = QuantumCircuit(n_qubits)
mask = "".join(["1" if n_qubits - 1 - k in pauli_index else "0"
for k in range(n_qubits)])
for single_pauli, index in zip(pauli_id, pauli_index):
if single_pauli == 1:
measurement_circuit.add_H_gate(index)
elif single_pauli == 2:
measurement_circuit.add_Sdag_gate(index)
measurement_circuit.add_H_gate(index)
measurement_circuit.update_quantum_state(buf_state)
samples = buf_state.sampling(n_sample)
mask = int(mask, 2)
exp += (coef
*sum(list(map(lambda x: (-1)**(bin(x & mask).count("1")),
samples)))
/n_sample)
return exp
def sample_observable(state, obs, n_sample):
"""
Args:
state (qulacs.QuantumState):
obs (qulacs.Observable)
n_sample (int): number of samples for each observable
Return:
:float: sampled expectation value of the observable
"""
n_term = obs.get_term_count()
n_qubit = obs.get_qubit_count()
pauli_terms = [obs.get_term(i) for i in range(n_term)]
coefs = [p.get_coef() for p in pauli_terms]
pauli_ids = [p.get_pauli_id_list() for p in pauli_terms]
pauli_indices = [p.get_index_list() for p in pauli_terms]
exp = 0
measured_state = state.copy()
for i in range(n_term):
state.load(measured_state)
measurement_circuit = QuantumCircuit(n_qubit)
if len(pauli_ids[i]) == 0: # means identity
exp += coefs[i]
continue
mask = ''.join([
'1' if n_qubit - 1 - k in pauli_indices[i] else '0'
for k in range(n_qubit)
])
for single_pauli, index in zip(pauli_ids[i], pauli_indices[i]):
if single_pauli == 1:
measurement_circuit.add_H_gate(index)
elif single_pauli == 2:
measurement_circuit.add_Sdag_gate(index)
measurement_circuit.add_H_gate(index)
measurement_circuit.update_quantum_state(state)
samples = state.sampling(n_sample)
mask = int(mask, 2)
exp += coefs[i] * sum(
list(map(lambda x:
(-1)**(bin(x & mask).count('1')), samples))) / n_sample
return exp
def adaptive_sample_observable(state, obs, n_sample):
"""
Args:
state (qulacs.QuantumState):
obs (qulacs.Observable)
n_sample (int): number of samples for each observable
Return:
:float: sampled expectation value of the observable
"""
n_term = obs.get_term_count()
n_qubits = obs.get_qubit_count()
exp = 0
buf_state = QuantumState(n_qubits)
### check the coefficients for each term...
coef_list = np.array([abs(obs.get_term(i).get_coef())
for i in range(n_term)])
sum_coef = np.sum(coef_list)
### sort
sorted_indices = np.argsort(-coef_list)
coef_list.sort()
#sorted_coef_list = [coef_list[i] for i in sorted_indices]
### determine sampling wight
n_sample_total = n_sample*n_term
n_sample_list = n_sample_total*coef_list//sum_coef
n_count = np.sum(n_sample_list)
n_rest = n_sample_total - n_count
n_sample_list[sorted_indices[:n_rest]] += 1
j = 0
for i in range(n_term):
if n_sample_list[i] == 0:
continue
j += n_sample_list[i]
pauli_term = obs.get_term(i)
coef = pauli_term.get_coef()
pauli_id = pauli_term.get_pauli_id_list()
pauli_index = pauli_term.get_index_list()
if len(pauli_id) == 0: # means identity
exp += coef
continue
buf_state.load(state)
measurement_circuit = QuantumCircuit(n_qubits)
mask = "".join(["1" if n_qubits - 1 - k in pauli_index else "0"
for k in range(n_qubits)])
for single_pauli, index in zip(pauli_id, pauli_index):
if single_pauli == 1:
measurement_circuit.add_H_gate(index)
elif single_pauli == 2:
measurement_circuit.add_Sdag_gate(index)
measurement_circuit.add_H_gate(index)
measurement_circuit.update_quantum_state(buf_state)
samples = buf_state.sampling(n_sample_list[i])
mask = int(mask, 2)
exp += (coef
*sum(list(map(lambda x: (-1)**(bin(x & mask).count("1")),
samples)))
/n_sample_list[i])
return exp
def test_transition_observable(state, obs, poststate0, poststate1, n_sample):
"""
Args:
state (qulacs.QuantumState): This includes entangled ancilla
(n_qubits = n_qubit_system + 1)
obs (qulacs.Observable): This does not include ancilla Z
(n_qubit_system)
poststate0 (qulacs.QuantumState): post-measurement state
when ancilla = 0 (n_qubit_system)
poststate1 (qulacs.QuantumState): post-measurement state
when ancilla = 1 (n_qubit_system)
n_sample (int): number of samples for each observable
Return:
:float: sampled expectation value of the observable
"""
n_term = obs.get_term_count()
n_qubits = obs.get_qubit_count()
p0 = state.get_zero_probability(n_qubits - 1)
p1 = 1 - p0
opt = f"0{n_qubits}b"
prints(f"p0: {p0} p1: {p1}")
print_state(poststate0, name="post(0)")
prints("post(1)")
print_state(poststate1, name="post(1)")
expH = 0
exp = []
coef = []
buf_state = QuantumState(n_qubits)
for i in range(n_term):
pauli_term = obs.get_term(i)
coef.append(pauli_term.get_coef().real)
pauli_id = pauli_term.get_pauli_id_list()
pauli_index = pauli_term.get_index_list()
if len(pauli_id) == 0: # means identity
exp.extend(coef)
continue
buf_state.load(state)
measurement_circuit = QuantumCircuit(n_qubits)
mask = "".join(["1" if n_qubits - 1 - k in pauli_index else "0"
for k in range(n_qubits)])
measure_observable = QubitOperator((), 1)
#measure_observable = QubitOperator('Z%d' % n_qubits)
for single_pauli, index in zip(pauli_id, pauli_index):
if single_pauli == 1:
### X
measurement_circuit.add_H_gate(index)
measure_observable *= QubitOperator(f"X{index}")
elif single_pauli == 2:
### Y
measurement_circuit.add_Sdag_gate(index)
measurement_circuit.add_H_gate(index)
measure_observable *= QubitOperator(f"Y{index}")
elif single_pauli == 3:
### Z
measure_observable *= QubitOperator(f"Z{index}")
qulacs_measure_observable \
= create_observable_from_openfermion_text(
str(measure_observable))
### p0 ###
H0 = qulacs_measure_observable.get_expectation_value(poststate0)
### p1 ###
H1 = qulacs_measure_observable.get_expectation_value(poststate1)
prob = p0*H0 - p1*H1
# print(prob, qulacs_measure_observable.get_expectation_value(state), obs.get_expectation_value(state))
prob = qulacs_measure_observable.get_expectation_value(state)
expH += coef[i]*prob
# measurement_circuit.update_quantum_state(buf_state)
# samples = buf_state.sampling(n_sample)
# print('samples? ',format(samples[0],opt))
# print("I = :",'%5d' % i, " h_I ", '%10.5f' % coef[i], " <P_I> ", '%10.5f' % exp[i])
# mask = int(mask, 2)
# print(sum(list(map(lambda x: (-1) **(bin(x & mask).count('1')), samples))))
# print(coef*sum(list(map(lambda x: (-1) **
# (bin(x & mask).count('1')), samples))))
# expH += coef[i] * exp[i]
# samples = buf_state.sampling(n_sample)
# mask = int(mask, 2)
# prob = sum(list(map(lambda x: (-1) **
# (bin(x & mask).count('1')), samples)))/n_sample
# measure_list = list(map(int,np.ones(n_qubits)*2))
# for j in pauli_index:
# measure_list[j] = 1
# print(qulacs_measure_observable.get_expectation_value(state))
# expH += coef[i] * prob
print(f"coef: {coef[i]:10.5f} prob: {prob:10.5f}")
return expH
def test_observable(state, obs, obsZ, n_sample):
"""Function
Args:
state (qulacs.QuantumState): This includes entangled ancilla
(n_qubits = n_qubit_system + 1)
obs (qulacs.Observable): This does not include ancilla Z
(n_qubit_system)
obsZ (qulacs.Observable): Single Pauli Z for ancilla (1)
poststate0 (qulacs.QuantumState): post-measurement state
when ancilla = 0 (n_qubit_system)
poststate1 (qulacs.QuantumState): post-measurement state
when ancilla = 1 (n_qubit_system)
n_sample (int): number of samples for each observable
Return:
:float: sampled expectation value of the observable
Author(s): Takashi Tsuchimochi
"""
n_term = obs.get_term_count()
n_qubits = obs.get_qubit_count()
p0 = state.get_zero_probability(n_qubits)
p1 = 1 - p0
opt = f"0{n_qubits}b"
expH = 0
exp = []
coef = []
buf_state = QuantumState(n_qubits)
for i in range(n_term):
pauli_term = obs.get_term(i)
coef.append(pauli_term.get_coef().real)
pauli_id = pauli_term.get_pauli_id_list()
pauli_index = pauli_term.get_index_list()
if len(pauli_id) == 0: # means identity
exp.extend(coef)
continue
buf_state.load(state)
measurement_circuit = QuantumCircuit(n_qubits)
mask = "".join(["1" if n_qubits - 1 - k in pauli_index else "0"
for k in range(n_qubits)])
measure_observable = QubitOperator((), 1)
for single_pauli, index in zip(pauli_id, pauli_index):
if single_pauli == 1:
### X
measurement_circuit.add_H_gate(index)
measure_observable *= QubitOperator(f"X{index}")
elif single_pauli == 2:
### Y
measurement_circuit.add_Sdag_gate(index)
measurement_circuit.add_H_gate(index)
measure_observable *= QubitOperator(f"Y{index}")
elif single_pauli == 3:
### Z
measure_observable *= QubitOperator(f"Z{index}")
qulacs_measure_observable \
= create_observable_from_openfermion_text(
str(measure_observable))
measurement_circuit.update_quantum_state(buf_state)
#exp.append(obsZ.get_expectation_value(buf_state).real)
samples = buf_state.sampling(n_sample)
#print(f"samples? {format(samples[0], opt)}")
#print(f"I = {i:5d} h_I = {coef[i]:10.5f} <P_I> = {exp[i]:10.5f}")
#mask = int(mask, 2)
#print(sum(list(map(lambda x: (-1)**(bin(x & mask).count('1')),
# samples))))
#print(coef*sum(list(map(lambda x: (-1)**(bin(x & mask).count('1')),
# samples))))
expH += coef[i]*exp[i]
samples = buf_state.sampling(n_sample)
mask = int(mask, 2)
prob = (sum(list(map(lambda x: (-1)**(bin(x & mask).count("1")),
samples)))
/n_sample)
measure_list = list(map(int, np.ones(n_qubits)*2))
for j in pauli_index:
measure_list[j] = 1
#print(qulacs_measure_observable.get_expectation_value(state))
expH += coef[i]*prob
#print(f"coef: {coef[i]:10.5f} prob: {prob:10.5f}")
return expH