def test_save_expval_var_cptp_pauli(self, pauli):
"""Test Pauli expval_var for stabilizer circuit"""
SUPPORTED_METHODS = [
'density_matrix', 'density_matrix_gpu', 'density_matrix_thrust'
]
SEED = 5832
opts = self.BACKEND_OPTS.copy()
if opts.get('method') in SUPPORTED_METHODS:
oper = qi.Operator(qi.Operator(qi.Pauli(pauli)))
# CPTP channel test circuit
channel = qi.random_quantum_channel(4, seed=SEED)
state_circ = QuantumCircuit(2)
state_circ.append(channel, range(2))
state = qi.DensityMatrix(state_circ)
expval = state.expectation_value(oper).real
variance = state.expectation_value(oper**2).real - expval**2
target = [expval, variance]
# Snapshot circuit
circ = transpile(state_circ, self.SIMULATOR)
circ.save_expectation_value_variance(oper, [0, 1], label='expval')
qobj = assemble(circ)
result = self.SIMULATOR.run(qobj, **opts).result()
self.assertTrue(result.success)
value = result.data(0)['expval']
self.assertTrue(allclose(value, target))
def test_save_unitary(self):
"""Test save unitary for instruction"""
SUPPORTED_METHODS = [
'automatic', 'unitary', 'unitary_gpu', 'unitary_thrust'
]
# Stabilizer test circuit
circ = transpile(QuantumVolume(3), self.SIMULATOR)
# Target unitary
target = qi.Operator(circ)
# Add save to circuit
save_key = 'state'
circ.save_unitary(save_key)
# Run
opts = self.BACKEND_OPTS.copy()
qobj = assemble(circ, self.SIMULATOR)
result = self.SIMULATOR.run(qobj, **opts).result()
method = opts.get('method', 'automatic')
if method not in SUPPORTED_METHODS:
self.assertFalse(result.success)
else:
self.assertTrue(result.success)
data = result.data(0)
self.assertIn(save_key, data)
value = qi.Operator(result.data(0)[save_key])
self.assertEqual(value, target)
def test_weyl_unitaries_random_circuit(self):
"""Weyl decomposition for a random two-qubit circuit."""
theta = pi / 9
epsilon = 5
delta = -1
eta = 0.2
qr = QuantumRegister(2, "qr")
circuit = QuantumCircuit(qr)
# random two-qubit circuit.
circuit.rzx(theta, 0, 1)
circuit.rzz(epsilon, 0, 1)
circuit.rz(eta, 0)
circuit.swap(1, 0)
circuit.h(0)
circuit.rzz(delta, 1, 0)
circuit.swap(0, 1)
circuit.cx(1, 0)
circuit.swap(0, 1)
circuit.h(1)
circuit.rxx(theta, 0, 1)
circuit.ryy(theta, 1, 0)
circuit.ecr(0, 1)
unitary_circuit = qi.Operator(circuit).data
dag = circuit_to_dag(circuit)
pass_ = EchoRZXWeylDecomposition(self.inst_map)
after = dag_to_circuit(pass_.run(dag))
unitary_after = qi.Operator(after).data
self.assertTrue(np.allclose(unitary_circuit, unitary_after))
def test_save_expval_var_cptp_pauli(self, method, device, pauli):
"""Test Pauli expval_var for stabilizer circuit"""
SEED = 5832
oper = qi.Operator(qi.Operator(qi.Pauli(pauli)))
channel = qi.random_quantum_channel(4, seed=SEED)
circ = QuantumCircuit(2)
circ.append(channel, range(2))
qubits = [0, 1]
self._test_save_expval(circ,
oper,
qubits,
True,
method=method,
device=device)
def test_weyl_decomposition_gate_angles(self):
"""Check the number and angles of the RZX gates for different gates"""
thetas = [pi / 9, 2.1, -0.2]
qr = QuantumRegister(2, "qr")
circuit_rxx = QuantumCircuit(qr)
circuit_rxx.rxx(thetas[0], qr[1], qr[0])
circuit_ryy = QuantumCircuit(qr)
circuit_ryy.ryy(thetas[1], qr[0], qr[1])
circuit_rzz = QuantumCircuit(qr)
circuit_rzz.rzz(thetas[2], qr[1], qr[0])
circuits = [circuit_rxx, circuit_ryy, circuit_rzz]
for circuit in circuits:
unitary_circuit = qi.Operator(circuit).data
dag = circuit_to_dag(circuit)
pass_ = EchoRZXWeylDecomposition(self.inst_map)
after = dag_to_circuit(pass_.run(dag))
dag_after = circuit_to_dag(after)
unitary_after = qi.Operator(after).data
# check whether the unitaries are equivalent.
self.assertTrue(np.allclose(unitary_circuit, unitary_after))
# check whether the after circuit has the correct number of rzx gates.
self.assertRZXgates(unitary_circuit, after)
alpha = TwoQubitWeylDecomposition(unitary_circuit).a
rzx_angles = []
for node in dag_after.two_qubit_ops():
if node.name == "rzx":
rzx_angle = node.op.params[0]
# check whether the absolute values of the RZX gate angles
# are equivalent to the corresponding Weyl parameter.
self.assertAlmostEqual(np.abs(rzx_angle), alpha)
rzx_angles.append(rzx_angle)
# check whether the angles of every RZX gate pair of an echoed RZX gate
# have opposite signs.
for idx in range(1, len(rzx_angles), 2):
self.assertAlmostEqual(rzx_angles[idx - 1], -rzx_angles[idx])
def hamiltonian_superop(ham):
ham = qi.Operator(ham)
dim, _ = ham.dim
iden = np.eye(dim)
super_op = -1j * np.kron(iden, ham.data) + 1j * np.kron(
np.conj(ham.data), iden)
return qi.SuperOp(super_op)
def test_rzx_number_native_weyl_decomposition(self):
"""Check the number of RZX gates for a hardware-native cx"""
qr = QuantumRegister(2, "qr")
circuit = QuantumCircuit(qr)
circuit.cx(qr[0], qr[1])
unitary_circuit = qi.Operator(circuit).data
after = EchoRZXWeylDecomposition(self.inst_map)(circuit)
unitary_after = qi.Operator(after).data
self.assertTrue(np.allclose(unitary_circuit, unitary_after))
# check whether the after circuit has the correct number of rzx gates.
self.assertRZXgates(unitary_circuit, after)
def test_save_expval_var_stabilizer_pauli(self, pauli):
"""Test Pauli expval_var for stabilizer circuit"""
SUPPORTED_METHODS = [
'automatic', 'statevector', 'statevector_gpu',
'statevector_thrust', 'density_matrix', 'density_matrix_gpu',
'density_matrix_thrust', 'matrix_product_state', 'stabilizer'
]
SEED = 5832
# Stabilizer test circuit
state_circ = qi.random_clifford(2, seed=SEED).to_circuit()
oper = qi.Operator(qi.Pauli(pauli))
state = qi.Statevector(state_circ)
expval = state.expectation_value(oper).real
variance = state.expectation_value(oper**2).real - expval**2
target = [expval, variance]
# Snapshot circuit
opts = self.BACKEND_OPTS.copy()
method = opts.get('method', 'automatic')
circ = transpile(state_circ,
basis_gates=[
'id', 'x', 'y', 'z', 'h', 's', 'sdg', 'cx', 'cz',
'swap'
])
circ.save_expectation_value_variance(oper, [0, 1], label='expval')
qobj = assemble(circ)
result = self.SIMULATOR.run(qobj, **opts).result()
if method not in SUPPORTED_METHODS:
self.assertFalse(result.success)
else:
self.assertTrue(result.success)
value = result.data(0)['expval']
self.assertTrue(allclose(value, target))
def test_save_expval_nonstabilizer_pauli(self, pauli):
"""Test Pauli expval for non-stabilizer circuit"""
SUPPORTED_METHODS = [
'automatic', 'statevector', 'statevector_gpu',
'statevector_thrust', 'density_matrix', 'density_matrix_gpu',
'density_matrix_thrust', 'matrix_product_state'
]
SEED = 7382
# Stabilizer test circuit
state_circ = QuantumVolume(2, 1, seed=SEED)
oper = qi.Operator(qi.Pauli(pauli))
state = qi.Statevector(state_circ)
target = state.expectation_value(oper).real
# Snapshot circuit
opts = self.BACKEND_OPTS.copy()
method = opts.get('method', 'automatic')
circ = transpile(state_circ,
basis_gates=['u1', 'u2', 'u3', 'cx', 'swap'])
circ.save_expectation_value(oper, [0, 1], label='expval')
qobj = assemble(circ)
result = self.SIMULATOR.run(qobj, **opts).result()
if method not in SUPPORTED_METHODS:
self.assertFalse(result.success)
else:
self.assertTrue(result.success)
value = result.data(0)['expval']
self.assertAlmostEqual(value, target)
def _test_save_expval(self, circuit, oper, qubits, variance, **options):
"""Test Pauli expval for stabilizer circuit"""
backend = self.backend(**options)
label = 'expval'
# Format operator and target value
circ = circuit.copy()
oper = qi.Operator(oper)
state = qi.DensityMatrix(circ)
expval = state.expectation_value(oper, qubits).real
if variance:
var = state.expectation_value(oper**2, qubits).real - expval**2
target = [expval, var]
circ.save_expectation_value_variance(oper, qubits, label=label)
else:
target = expval
circ.save_expectation_value(oper, qubits, label=label)
result = backend.run(transpile(circ, backend, optimization_level=0),
shots=1).result()
self.assertTrue(result.success)
simdata = result.data(0)
self.assertIn(label, simdata)
value = simdata[label]
if variance:
self.assertTrue(allclose(value, target))
else:
self.assertAlmostEqual(value, target)
def assert_circuit_equivalence(self, qc, qcd):
""" Raise exception if two circuits not equivalent """
I = qc.compose(qcd.inverse())
op = qi.Operator(I)
U = op.data / np.sqrt(complex(np.linalg.det(op.data)))
U *= U[0, 0]
np.testing.assert_almost_equal(U, np.eye(2**qc.num_qubits))
def test_pauli_error_2q_gate_from_string_1qonly(self):
"""Test two-qubit pauli error as gate qobj from string label"""
paulis = ['XI', 'YI', 'ZI']
probs = [0.5, 0.3, 0.2]
with self.assertWarns(DeprecationWarning):
actual = pauli_error(zip(paulis, probs), standard_gates=True)
target_circs = [[{"name": "id", "qubits": [0]}, {"name": "x", "qubits": [1]}],
[{"name": "id", "qubits": [0]}, {"name": "y", "qubits": [1]}],
[{"name": "id", "qubits": [0]}, {"name": "z", "qubits": [1]}]]
with self.assertWarns(DeprecationWarning):
expected = QuantumError(zip(target_circs, probs), standard_gates=True)
for i in range(actual.size):
circ, prob = actual.error_term(i)
expected_circ, expected_prob = expected.error_term(i)
self.assertTrue(qi.Operator(circ).equiv(qi.Operator(expected_circ)))
self.assertAlmostEqual(prob, expected_prob)
def _test_gate(self, gate, gates_dict, **options):
"""Test standard gates."""
backend = self.backend(**options)
gate_cls, num_angles, has_ctrl_qubits = gates_dict[gate]
circuits = self.gate_circuits(gate_cls,
num_angles=num_angles,
has_ctrl_qubits=has_ctrl_qubits,
rng=self.RNG)
label = 'final'
method = backend.options.method
for circuit in circuits:
if method == 'density_matrix':
target = qi.DensityMatrix(circuit)
circuit.save_density_matrix(label=label)
state_fn = qi.DensityMatrix
fidelity_fn = qi.state_fidelity
elif method == 'stabilizer':
target = qi.Clifford(circuit)
circuit.save_stabilizer(label=label)
state_fn = qi.Clifford.from_dict
fidelity_fn = qi.process_fidelity
elif method == 'unitary':
target = qi.Operator(circuit)
circuit.save_unitary(label=label)
state_fn = qi.Operator
fidelity_fn = qi.process_fidelity
elif method == 'superop':
target = qi.SuperOp(circuit)
circuit.save_superop(label=label)
state_fn = qi.SuperOp
fidelity_fn = qi.process_fidelity
else:
target = qi.Statevector(circuit)
circuit.save_statevector(label=label)
state_fn = qi.Statevector
fidelity_fn = qi.state_fidelity
result = backend.run(transpile(circuit,
backend,
optimization_level=0),
shots=1).result()
# Check results
success = getattr(result, 'success', False)
self.assertTrue(success)
data = result.data(0)
self.assertIn(label, data)
value = state_fn(data[label])
fidelity = fidelity_fn(target, value)
self.assertGreater(fidelity, 0.9999)
def test_save_expval_var_stabilizer_pauli(self, method, device, pauli):
"""Test Pauli expval_var for stabilizer circuit"""
SEED = 5832
circ = qi.random_clifford(2, seed=SEED).to_circuit()
oper = qi.Operator(qi.Pauli(pauli))
qubits = [0, 1]
self._test_save_expval(circ,
oper,
qubits,
True,
method=method,
device=device)
def test_save_expval_var_nonstabilizer_pauli(self, method, device, pauli):
"""Test Pauli expval_var for non-stabilizer circuit"""
SEED = 7382
circ = QuantumVolume(2, 1, seed=SEED)
oper = qi.Operator(qi.Pauli(pauli))
qubits = [0, 1]
self._test_save_expval(circ,
oper,
qubits,
True,
method=method,
device=device)
def _target_quantum_channel(
cls,
circuit: QuantumCircuit,
measurement_qubits: Optional[Sequence[int]] = None,
preparation_qubits: Optional[Sequence[int]] = None,
):
"""Return the process tomography target"""
# Check if circuit contains measure instructions
# If so we cannot return target state
circuit_ops = circuit.count_ops()
if "measure" in circuit_ops:
return None
perm_circ = cls._permute_circuit(circuit,
measurement_qubits=measurement_qubits,
preparation_qubits=preparation_qubits)
try:
if "reset" in circuit_ops or "kraus" in circuit_ops or "superop" in circuit_ops:
channel = qi.Choi(perm_circ)
else:
channel = qi.Operator(perm_circ)
except QiskitError:
# Circuit couldn't be simulated
return None
total_qubits = circuit.num_qubits
if measurement_qubits:
num_meas = len(measurement_qubits)
else:
num_meas = total_qubits
if preparation_qubits:
num_prep = len(preparation_qubits)
else:
num_prep = total_qubits
if num_prep == total_qubits and num_meas == total_qubits:
return channel
# Trace out non-measurement subsystems
tr_qargs = []
if preparation_qubits:
tr_qargs += list(range(num_prep, total_qubits))
if measurement_qubits:
tr_qargs += list(range(total_qubits + num_meas, 2 * total_qubits))
chan_state = qi.Statevector(np.ravel(channel, order="F"))
chan_state = qi.partial_trace(chan_state,
tr_qargs) / 2**(total_qubits - num_meas)
channel = qi.Choi(chan_state.data,
input_dims=[2] * num_prep,
output_dims=[2] * num_meas)
return channel
def run(self, dag: DAGCircuit):
"""Run the EchoRZXWeylDecomposition pass on `dag`.
Rewrites two-qubit gates in an arbitrary circuit in terms of echoed cross-resonance
gates by computing the Weyl decomposition of the corresponding unitary. Modifies the
input dag.
Args:
dag (DAGCircuit): DAG to rewrite.
Returns:
DAGCircuit: The modified dag.
Raises:
TranspilerError: If the circuit cannot be rewritten.
"""
if len(dag.qregs) > 1:
raise TranspilerError(
"EchoRZXWeylDecomposition expects a single qreg input DAG,"
f"but input DAG had qregs: {dag.qregs}.")
trivial_layout = Layout.generate_trivial_layout(*dag.qregs.values())
decomposer = TwoQubitControlledUDecomposer(RZXGate)
for node in dag.two_qubit_ops():
unitary = qi.Operator(node.op).data
dag_weyl = circuit_to_dag(decomposer(unitary))
dag.substitute_node_with_dag(node, dag_weyl)
for node in dag.two_qubit_ops():
if node.name == "rzx":
control = node.qargs[0]
target = node.qargs[1]
physical_q0 = trivial_layout[control]
physical_q1 = trivial_layout[target]
is_native = self._is_native((physical_q0, physical_q1))
theta = node.op.params[0]
if is_native:
dag.substitute_node_with_dag(node,
self._echo_rzx_dag(theta))
else:
dag.substitute_node_with_dag(
node, self._reverse_echo_rzx_dag(theta))
return dag
def test_save_unitary(self, method, device):
"""Test save unitary instruction"""
backend = self.backend(method=method, device=device)
# Test circuit
SEED = 5426
circ = QuantumVolume(3, seed=SEED)
# Target unitary
target = qi.Operator(circ)
# Add save to circuit
label = 'state'
circ.save_unitary(label=label)
# Run
result = backend.run(transpile(
circ, backend, optimization_level=0), shots=1).result()
self.assertTrue(result.success)
simdata = result.data(0)
self.assertIn(label, simdata)
value = qi.Operator(simdata[label])
self.assertEqual(value, target)
def test_save_expval_stabilizer_pauli_cache_blocking(
self, method, device, pauli):
"""Test Pauli expval for stabilizer circuit"""
SEED = 5832
circ = qi.random_clifford(2, seed=SEED).to_circuit()
oper = qi.Operator(qi.Pauli(pauli))
qubits = [0, 1]
self._test_save_expval(circ,
oper,
qubits,
False,
method=method,
device=device,
blocking_qubits=2,
max_parallel_threads=1)
def test_unitary_snap(self):
"""Test Unitary matrix snaps on a random circuit"""
backend = UnitarySimulator()
target = qi.random_unitary(2 ** 4, seed=111)
circ = QuantumCircuit(4)
circ.append(target, [0, 1, 2, 3])
circ.append(Snapshot("final", "unitary", 4), [0, 1, 2, 3])
qobj = assemble(circ, backend=backend, shots=1)
job = backend.run(qobj)
result = job.result()
self.assertSuccess(result)
snaps = result.data(0)['snapshots']['unitary']['final']
for arr in snaps:
self.assertTrue(isinstance(arr, np.ndarray))
self.assertEqual(qi.Operator(arr), target)
def test_full_exp_meas_prep_qubits(self, qubits):
"""Test subset state tomography generation"""
# Subsystem unitaries
seed = 1111
nq = 3
ops = [qi.random_unitary(2, seed=seed + i) for i in range(nq)]
# Target state
target_circ = QuantumCircuit(len(qubits))
for i, qubit in enumerate(qubits):
target_circ.append(ops[qubit], [i])
target = qi.Operator(target_circ)
# Preparation circuit
circ = QuantumCircuit(nq)
for i, op in enumerate(ops):
circ.append(op, [i])
# Run
backend = AerSimulator(seed_simulator=9000)
exp = ProcessTomography(circ,
measurement_qubits=qubits,
preparation_qubits=qubits)
expdata = exp.run(backend)
self.assertExperimentDone(expdata)
results = expdata.analysis_results()
# Check result
f_threshold = 0.95
# Check state is density matrix
state = filter_results(results, "state").value
self.assertTrue(isinstance(state, qi.Choi),
msg="fitted state is not a Choi matrix")
# Check fit state fidelity
fid = filter_results(results, "process_fidelity").value
self.assertGreater(fid, f_threshold, msg="fit fidelity is low")
# Manually check fidelity
target_fid = qi.process_fidelity(state,
target,
require_tp=False,
require_cp=False)
self.assertAlmostEqual(fid,
target_fid,
places=6,
msg="result fidelity is incorrect")
def generate_two_qubit_N_operator(theta):
'''
somehow this is diff from the commented out one above lol ohwell
this is from Abol's paper
'''
qc = QuantumCircuit(2, name = "N({theta})".format(theta = theta))
qc.rz(np.pi/2,1)
qc.cx(1,0)
qc.rz(2*theta - np.pi/2, 0)
qc.ry(np.pi/2 - 2*theta, 1)
qc.cx(0,1)
qc.ry(2*theta - np.pi/2, 1)
qc.cx(1,0)
qc.rz(-np.pi/2,0)
return qi.Operator(qc)
def test_pauli_gate(self, method, device, pauli):
"""Test multi-qubit Pauli gate."""
pauli = qi.Pauli(pauli)
circuit = QuantumCircuit(pauli.num_qubits)
circuit.append(pauli, range(pauli.num_qubits))
backend = self.backend(method=method, device=device)
label = 'final'
if method == 'density_matrix':
target = qi.DensityMatrix(circuit)
circuit.save_density_matrix(label=label)
state_fn = qi.DensityMatrix
fidelity_fn = qi.state_fidelity
elif method == 'stabilizer':
target = qi.Clifford(circuit)
circuit.save_stabilizer(label=label)
state_fn = qi.Clifford.from_dict
fidelity_fn = qi.process_fidelity
elif method == 'unitary':
target = qi.Operator(circuit)
circuit.save_unitary(label=label)
state_fn = qi.Operator
fidelity_fn = qi.process_fidelity
elif method == 'superop':
target = qi.SuperOp(circuit)
circuit.save_superop(label=label)
state_fn = qi.SuperOp
fidelity_fn = qi.process_fidelity
else:
target = qi.Statevector(circuit)
circuit.save_statevector(label=label)
state_fn = qi.Statevector
fidelity_fn = qi.state_fidelity
result = backend.run(transpile(circuit, backend, optimization_level=0),
shots=1).result()
# Check results
success = getattr(result, 'success', False)
self.assertTrue(success)
data = result.data(0)
self.assertIn(label, data)
value = state_fn(data[label])
fidelity = fidelity_fn(target, value)
self.assertGreater(fidelity, 0.9999)
def costvsthetas_disc(vth):
th1 = np.round(vth[0]) / 32 * pi
th2 = np.round(vth[1]) / 32 * pi
th3 = np.round(vth[2]) / 32 * pi
th4 = np.round(vth[3]) / 32 * pi
qc = QuantumCircuit(4)
qc.rx(th1, 0)
qc.rx(th2, 1)
qc.rx(th3, 2)
qc.rx(th4, 3)
mtrx = qi.Operator(qc).data
#mtrx = fourgates(th1, th2, th3, th4)
return cost(mtrx - uu)
def test_set_unitary(self, method, device, num_qubits):
"""Test SetUnitary instruction"""
backend = self.backend(method=method, device=device)
seed = 100
label = 'state'
target = qi.random_unitary(2**num_qubits, seed=seed)
circ = QuantumCircuit(num_qubits)
circ.set_unitary(target)
circ.save_unitary(label=label)
# Run
result = backend.run(transpile(circ, backend, optimization_level=0),
shots=1).result()
self.assertTrue(result.success)
simdata = result.data(0)
self.assertIn(label, simdata)
value = qi.Operator(simdata[label])
self.assertEqual(value, target)
def test_exp_measurement_preparation_qubits(self, qubits):
"""Test subset measurement process tomography generation"""
# Subsystem unitaries
seed = 1111
nq = 3
ops = [qi.random_unitary(2, seed=seed + i) for i in range(nq)]
# Preparation circuit
circ = QuantumCircuit(nq)
for i, op in enumerate(ops):
circ.append(op, [i])
num_meas = len(qubits)
exp = ProcessTomography(circ,
measurement_qubits=qubits,
preparation_qubits=qubits)
tomo_circuits = exp.circuits()
# Check correct number of circuits are generated
size = 3**num_meas * 4**num_meas
self.assertEqual(len(tomo_circuits), size)
# Check circuit metadata is correct
for circ in tomo_circuits:
meta = circ.metadata
clbits = meta.get("clbits")
self.assertEqual(clbits,
list(range(num_meas)),
msg="metadata clbits is incorrect")
# Check experiment target metadata is correct
exp_meta = exp._metadata()
target_state = exp_meta.get("target")
target_circ = QuantumCircuit(num_meas)
for i, qubit in enumerate(qubits):
target_circ.append(ops[qubit], [i])
fid = qi.process_fidelity(target_state, qi.Operator(target_circ))
self.assertGreater(fid, 0.99, msg="target_state is incorrect")
def circ2matrix(qc=None):
#pl.figure() #figsize=(20,9))
pl.clf()
if not qc: qc = QuantumCircuit(4)
else:
uc = qi.Operator(qc).data
pl.subplot(121)
plu(uc)
pl.subplot(122)
plu(uc / compru(uc[0:2, 0:2]), ampl=False)
be = aer.get_backend('unitary_simulator')
ucompr = compru(u22)
gatestr = input('Next gate: ')
while gatestr != 'q':
if gatestr == 'r': qc = QuantumCircuit(4)
elif gatestr[0:3] != 'qc.':
try:
exec(gatestr)
except:
print('ignoring previous command')
else:
#exec('qc.'+gatestr.strip())
try:
exec(gatestr)
goodgate = True
except:
goodgate = False
print('ignoring this gate')
if goodgate:
uc = qi.Operator(qc).data
uc22 = uc[0:2, 0:2]
u4by4 = np.concatenate((uc22, uc22), axis=0)
u4by4 = np.concatenate((u4by4, u4by4), axis=1)
xuc22 = X @ uc22
x4by4 = np.concatenate((xuc22, xuc22), axis=0)
x4by4 = np.concatenate((x4by4, x4by4), axis=1)
u8by8 = np.concatenate((u4by4, x4by4), axis=1)
u8by8 = np.concatenate(
(u8by8, np.concatenate((x4by4, u4by4), axis=1)), axis=0)
compr = np.concatenate((np.concatenate(
(u8by8, u8by8),
axis=1), np.concatenate((u8by8, u8by8), axis=1)),
axis=0)
"""
pl.subplot(221)
plu(uu)
pl.subplot(222)
plu(uu/ucompr)
"""
pl.clf()
pl.subplot(121)
plu(uc)
#pl.show(block=False)
pl.subplot(122)
plu(uc / compr, ampl=False)
#pl.show(block=False)
gatestr = input('Next gate: ')
def get_unitary(circuit: QuantumCircuit) -> np.ndarray:
V = qi.Operator(circuit).data
return V
def hamiltonian_reconstruction(channels: List[Choi],
pauli_labels: List[str],
gate_time: float,
phase_shifts: List[float] = None,
shifter_label: str = 'ZI',
sanity_check: bool = False)\
-> Tuple[Dict[str, np.ndarray], List[float]]:
""" Extract Pauli term coefficient from quantum channel.
Args:
channels: quantum channels to reconstruct Hamiltonian.
pauli_labels: name of Pauli terms
gate_time: duration of gate
phase_shifts: phase shift to unwrap 2pi uncertainty.
shifter_label: pauli term to shift.
sanity_check: do sanity check.
Additional information:
To remove 2pi uncertainty of Logm, we need decompose superop S to satisfy |M| < 2 pi.
S_H = exp(w * L_H) where L_H is superop of Pauli term shift.
According to BCH expansion::
M = logm(S. S_H)
= logm(exp(tG).exp(w L_H))
= tG + w L_H + t*w*[G, L_H] + O(2 coms)
M' = M - w L_H
Then Pauli coefficients are::
b = Tr[B^dag.M']
= t*Tr[B^dag.G] + t*w*Tr[B^dag.[G, L_H]] + O(2 coms)
= b_true + + t*w*Tr[B^dag.[G, L_H]] + O(2 coms)
When commutator of G and L_H is zero, b = b_true.
Optimizer finds w to calculate principal matrix log.
"""
threshold_san1 = 1e-3
threshold_san2 = 1e-1
def hamiltonian_superop(ham):
ham = qi.Operator(ham)
dim, _ = ham.dim
iden = np.eye(dim)
super_op = -1j * np.kron(iden, ham.data) + 1j * np.kron(
np.conj(ham.data), iden)
return qi.SuperOp(super_op)
if phase_shifts is None:
phase_shifts = [0 for _ in range(len(channels))]
coeffs = defaultdict(list)
estimated_hamiltonian_fidelities = []
for phase_shift, chan in zip(phase_shifts, channels):
sup_s = qi.SuperOp(chan)
sup_l_h = hamiltonian_superop(qi.Operator.from_label(shifter_label))
def logm(w):
sup_s_h = qi.SuperOp(la.expm(w * sup_l_h.data))
return la.logm((sup_s @ sup_s_h).data)
def cost_func(w):
gen_m = logm(w) - w * sup_l_h.data
target = qi.SuperOp(la.expm(gen_m))
if __HAS_DNORM:
return dnorm(sup_s - target)
# use 2-norm when old version qiskit is used. both cost functions perform comparably.
return la.norm(sup_s.data - target.data)
def log_constraint(w):
return 2 * np.pi - la.norm(logm(w))
cons = ({'type': 'ineq', 'fun': log_constraint})
opt_result = opt.minimize(cost_func,
x0=phase_shift,
constraints=cons,
method='SLSQP')
w_opt = opt_result.x[0]
# opt status
print('w_opt = %.3e, cost_func = %.3e, generator norm = %.3e' %
(w_opt, cost_func(w_opt), log_constraint(w_opt)))
# sanitary check 1
sup_s_h_opt = qi.SuperOp(la.expm(w_opt * sup_l_h.data))
com_norm = la.norm((sup_s @ sup_s_h_opt - sup_s_h_opt @ sup_s).data)
print('Commutator [S, S_H] norm = %.3e' % com_norm)
if sanity_check:
assert com_norm < threshold_san1
gen_m_opt = logm(w_opt) - w_opt * sup_l_h.data
for pauli_label in pauli_labels:
sup_b = hamiltonian_superop(
0.5 * qi.Operator.from_label(pauli_label).data)
sup_b_dag = sup_b.adjoint()
renorm = np.real(np.trace((sup_b_dag @ sup_b).data))
coeff = np.real(
np.trace(np.dot(gen_m_opt, sup_b_dag.data)) / renorm)
coeffs[pauli_label].append(coeff / gate_time)
# sanitary check 2
reconst_ham = np.zeros((4, 4))
for pauli_label in pauli_labels:
ham_op = 0.5 * qi.Operator.from_label(pauli_label).data
reconst_ham = reconst_ham + coeffs[pauli_label][-1] * ham_op
reconst_u = qi.Operator(la.expm(-1j * reconst_ham * gate_time))
u_fid = qi.average_gate_fidelity(chan, reconst_u)
estimated_hamiltonian_fidelities.append(u_fid)
if sanity_check:
assert 1 - u_fid < threshold_san2
# list -> ndarray
coeffs = dict(coeffs)
for pauli_label in coeffs.keys():
coeffs[pauli_label] = np.array(coeffs[pauli_label])
return coeffs, estimated_hamiltonian_fidelities
noise_transform_to_left_channel(L)
for i in range(len(L)):
if L[i].pulse_type == 'noise':
pulse_noise.append(L[i])
m = np.identity(2)
for i in reversed(range(len(pulse_noise))):
m = pulse_to_unitary(
pulse_noise[i], delta /
2) @ m # delta/2: 1/2 here because of Clifford decomposition
noise_unitary.append(m)
depol_str = []
for i in range(len(noise_unitary)):
ch = quantum_info.Operator(noise_unitary[i])
F_ave = quantum_info.average_gate_fidelity(ch)
p = (d * F_ave - 1) / (d - 1)
depol_str.append(p)
avg_depol_str.append(np.mean(depol_str))
depha_m = np.cos(delta) * I_1q - 1j * np.sin(delta) * Z_1q
depha_ch = quantum_info.Operator(depha_m)
F_depha = quantum_info.average_gate_fidelity(depha_ch)
p_depha = (d * F_depha - 1) / (d - 1)
depha_str.append(p_depha)
plot1 = plt.figure(1)
plt.plot(delta_list, depha_str, 'ro', markersize=2, label='channel noise')
plt.plot(delta_list,
avg_depol_str,
