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ex.py
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ex.py
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import time
import json
from matplotlib import pyplot
from math import ceil
from collections import defaultdict
from qiskit.compiler import transpile, assemble
from qiskit.providers.ibmq.managed import IBMQJobManager
import numpy
from qiskit.providers.aer import AerSimulator, StatevectorSimulator
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library.standard_gates import HGate, XGate, YGate, ZGate
import qiskit.quantum_info as qi
import qiskit
from qiskit import IBMQ
#constructs a circuit that can estimate <psi|u|psi> where |psi>=psi_prep|0> using the Hadamard test
#it can give either the real or imaginary part based on whether complex_test is False or True, respectively
def hadamard_test_circuit(u, psi_prep, complex_test=False):
u_controlled = u.control(1)
ht_circuit = QuantumCircuit(u_controlled.num_qubits, 1)
ht_circuit.h(0)
if complex_test:
ht_circuit.p(-numpy.pi / 2, 0)
ht_circuit.append(psi_prep, list(range(1, u_controlled.num_qubits)))
ht_circuit.append(u_controlled, list(range(u_controlled.num_qubits)))
ht_circuit.h(0)
ht_circuit.measure(0, 0)
return ht_circuit
def my_getcounts(counts, i):
if i in counts:
return counts[i]
else:
return 0
def hadamard_test_expval(counts, bias_matrix):
c0 = my_getcounts(counts, '0')
c1 = my_getcounts(counts, '1')
c0_corrected, c1_corrected = numpy.linalg.solve(bias_matrix, numpy.transpose(numpy.array([c0, c1])))
return ((c0_corrected - c1_corrected) / (c0 + c1))
#estimates <psi|u|psi> using an exact statevector simulator
#this gives the correct answer to more-or-less machine precision
def expval(u, psi_prep):
svsim = StatevectorSimulator()
psi_sv = qiskit.execute(psi_prep, svsim).result().get_statevector()
u_psi_sv = qiskit.execute(psi_prep.compose(u), svsim).result().get_statevector()
return numpy.vdot(psi_sv.data, u_psi_sv.data)
#estimates <psi|u|psi> using the hadamard test for both the real and imaginary parts
def hadamard_expval_circuits(u, psi_prep):
return [hadamard_test_circuit(u, psi_prep), hadamard_test_circuit(u, psi_prep, complex_test=True)]
#computes <y|x> using the hadamard test
def hadamard_inner_products(y_preps, x_preps, shots, backend, bias_matrices=defaultdict(lambda: numpy.matrix([[1.0, 0], [0, 1]])), zne_repeats=0, isreal=False):
hadamard_circs = []
for i in range(len(y_preps)):
qc = QuantumCircuit(x_preps[i].num_qubits)
qc.append(x_preps[i], list(range(x_preps[i].num_qubits)))
qc.append(y_preps[i].inverse(), list(range(x_preps[i].num_qubits)))
if isreal:
hadamard_circs.append(hadamard_expval_circuits(qc.to_gate(), y_preps[i])[0])
else:
hadamard_circs.extend(hadamard_expval_circuits(qc.to_gate(), y_preps[i]))
counts, transpiled_circs = run_circuits(hadamard_circs, backend, shots, zne_repeats=zne_repeats)
retval = []
for i in range(len(y_preps)):
q1 = transpiled_circs[-2][-1][1][0].index
q2 = transpiled_circs[-1][-1][1][0].index
if isreal:
retval.append(hadamard_test_expval(counts[i], bias_matrices[q1]))
else:
retval.append(complex(hadamard_test_expval(counts[2 * i + 0], bias_matrices[q1]),
hadamard_test_expval(counts[2 * i + 1], bias_matrices[q2])))
return retval
def measurement_bias_matrices(backend, shots):
if shots > 0:
bias_circuits = []
for qubit in range(backend.configuration().n_qubits):
qc = QuantumCircuit(backend.configuration().n_qubits, 1)
qc.measure(qubit, 0)
bias_circuits.append(qc)
qc = QuantumCircuit(backend.configuration().n_qubits, 1)
qc.x(qubit)
qc.measure(qubit, 0)
bias_circuits.append(qc)
counts, _ = run_circuits(bias_circuits, backend, shots, transpile_circs=False)
bias_matrices = {}
for i in range(backend.configuration().n_qubits):
A11 = my_getcounts(counts[2 * i], '0') / shots
A21 = my_getcounts(counts[2 * i], '1') / shots
A12 = my_getcounts(counts[2 * i + 1], '0') / shots
A22 = my_getcounts(counts[2 * i + 1], '1') / shots
bias_matrices[i] = numpy.matrix([[A11, A12], [A21, A22]])
return bias_matrices
else:
bias_matrices = {}
properties = backend.properties()
for i in range(backend.configuration().n_qubits):
p01 = properties.qubit_property(i)['prob_meas0_prep1'][0]
p10 = properties.qubit_property(i)['prob_meas1_prep0'][0]
A11 = 1.0 - p10
A21 = p10
A12 = p01
A22 = 1.0 - p01
bias_matrices[i] = numpy.matrix([[A11, A12], [A21, A22]])
return bias_matrices
return
def blowchunks(lst, chunk_size):
return [lst[i:i + chunk_size] for i in range(0, len(lst), chunk_size)]
def repeat_zne(circ, repeats):
new_circ = QuantumCircuit(circ.num_qubits, circ.num_clbits)
for inst, qargs, cargs in circ.data[0:-1]:#leave the last instruction off, which should be the measurement instruction
if inst.name != "sx":#skip the repeats for sx, since the inverse isn't in the basis gates
for i in range(repeats):
new_circ._append(inst, qargs, cargs)
new_circ._append(inst.inverse(), qargs, cargs)
new_circ._append(inst, qargs, cargs)
inst, qargs, cargs = circ.data[-1]#now add the measurement back on
new_circ._append(inst, qargs, cargs)
return new_circ
def run_circuits(circs, backend, shots, transpile_circs=True, zne_repeats=0):
if transpile_circs:
circs_transpiled = transpile(circs, backend=backend, optimization_level=3, seed_transpiler=0)#setting the seed is important for the ZNE
else:
circs_transpiled = circs
circs_transpiled = list(map(lambda x: repeat_zne(x, zne_repeats), circs_transpiled))
#circs_transpiled = transpile(circs, backend=backend, optimization_level=0, seed_transpiler=0)#now do the transpilation to get it back to the native gate set, but set the optimization level to 0
conf = backend.configuration()
experiments_per_circ = ceil(shots / conf.max_shots)
repeated_circs = [circ for circ in circs_transpiled for i in range(experiments_per_circ)]
if hasattr(conf, 'max_experiments'):
max_experiments = conf.max_experiments
else:
max_experiments = len(repeated_circs)
job_chunks = blowchunks(repeated_circs, max_experiments)
all_jobsets = []
for job_chunk in job_chunks:#send all the circuits off to run
all_jobsets.append(backend.run(job_chunk, shots=ceil(shots / experiments_per_circ)))
all_counts = []
for i in range(len(all_jobsets)):#get all the counts
result = all_jobsets[i].result()
for j in range(len(job_chunks[i])):
all_counts.append(result.get_counts(j))
collated_counts = []
for i in range(len(circs)):
collated_counts.append({'0': 0, '1': 0})
for j in range(experiments_per_circ):
these_counts = all_counts[j + i * experiments_per_circ]
collated_counts[-1]['0'] += my_getcounts(these_counts, '0')
collated_counts[-1]['1'] += my_getcounts(these_counts, '1')
return collated_counts, circs_transpiled
def rank1_batch(z_prep, b_prep, v_prep, u_prep, alpha, beta, shots, backend, **kwargs):
u1s = [z_prep, v_prep, v_prep, z_prep]
u2s = [b_prep, b_prep, u_prep, u_prep]
zb, vb, vu, zu = hadamard_inner_products(u1s, u2s, shots, backend, **kwargs)
return zb - alpha * beta * vb / (1 + alpha * beta * vu) * zu
def hadamards(n):
c = QuantumCircuit(n)
for i in range(n):
c.h(i)
return c
zx_exact = 1 / 2
IBMQ.load_account()
provider = IBMQ.get_provider(hub='ibm-q-lanl', group='lanl', project='quantum-optimiza')
#backend = provider.get_backend('ibmq_bogota')
#bogota = provider.get_backend('ibmq_bogota')
hardware = provider.get_backend('ibm_auckland')
#hardware = provider.get_backend('ibmq_montreal')
#backend = qiskit.providers.aer.QasmSimulator.from_backend(hardware)
backend = hardware
#bias_matrices = measurement_bias_matrices(backend, 10 ** 5)
bias_matrices = measurement_bias_matrices(backend, 0)
num_samples = 10 ** 5
results_exact_sim = []
results_hardware_sim = []
results_hardware_sim_me = []
results_hardware_sim_me_zne = []
alpha = 1
beta = 1
#ns = list(range(1, 27))
#ns = [2, 4, 8, 16, 26]
#ns = [26, 16, 12, 8, 4, 2]
#ns = [12, 8, 4, 2]
ns = [16, 20, 24, 26]
#ns = [26]
for n in ns:
print(n)
t0 = time.time()
z_prep = hadamards(n).to_gate()
b_prep = hadamards(n).to_gate()
u_prep = hadamards(n).to_gate()
v_prep = hadamards(n).to_gate()
zx_h = rank1_batch(z_prep, b_prep, v_prep, u_prep, alpha, beta, num_samples, backend, isreal=True)
results_hardware_sim.append(zx_h)
print(f"{zx_h}: relative error with {num_samples} samples: {numpy.abs(zx_h - zx_exact) / numpy.abs(zx_exact)} ({backend.name()})")
zx_h1 = rank1_batch(z_prep, b_prep, v_prep, u_prep, alpha, beta, num_samples, backend, bias_matrices=bias_matrices, isreal=True)
results_hardware_sim_me.append(zx_h1)
print(f"{zx_h1}: relative error with {num_samples} samples: {numpy.abs(zx_h1 - zx_exact) / numpy.abs(zx_exact)} ({backend.name()} + measurement error correction)")
zx_h3 = rank1_batch(z_prep, b_prep, v_prep, u_prep, alpha, beta, num_samples, backend, bias_matrices=bias_matrices, zne_repeats=1, isreal=True)
print(f"{zx_h3}: relative error with {num_samples} samples: {numpy.abs(zx_h3 - zx_exact) / numpy.abs(zx_exact)} ({backend.name()} + measurement error correction + 1 ZNE repeat)")
zx_zne = zx_h1 + (zx_h1 - zx_h3) / (1 - 3) * (0 - 1)
results_hardware_sim_me_zne.append(zx_zne)
print(f"{zx_zne}: relative error with {num_samples} samples: {numpy.abs(zx_zne - zx_exact) / numpy.abs(zx_exact)} (ZNE extrapolation)")
t1 = time.time()
print(t1 - t0, "seconds")
d = {'ns': ns, 'results_hardware_sim': results_hardware_sim, 'results_hardware_sim_me': results_hardware_sim_me, 'results_hardware_sim_me_zne': results_hardware_sim_me_zne}
with open(f"results_hardware_{ns}.json", 'w') as outfile:
json.dump(d, outfile)