def test_sample_circuit_with_seed():
decomp = _simple_pauli_deco_dict(0.7, simplify_paulis=True)
circ = Circuit([X.on(LineQubit(0)) for _ in range(10)])
expected = sample_circuit(circ, decomp, random_state=4)[0]
# Check we're not sampling the same operation every call to sample_sequence
assert len(set(expected.all_operations())) > 1
for _ in range(10):
sampled = sample_circuit(circ, decomp, random_state=4)[0]
assert _equal(sampled, expected)
def test_sample_circuit_random_state(seed, seed_type):
decomposition = _simple_pauli_deco_dict(0.5)
if isinstance(seed_type, np.random.RandomState):
seed = np.random.RandomState(seed)
circuit, sign, norm = sample_circuit(twoq_circ,
decomposition,
random_state=seed)
for _ in range(20):
if isinstance(seed_type, np.random.RandomState):
seed = np.random.RandomState(seed)
new_circuit, new_sign, new_norm = sample_circuit(twoq_circ,
decomposition,
random_state=seed)
assert _equal(new_circuit, circuit)
assert new_sign == sign
assert np.isclose(new_norm, norm)
def test_sample_circuit_choi(decomposition_dict: DecompositionDict):
"""Tests the sample_circuit by comparing the exact Choi matrices."""
ideal_choi = _circuit_to_choi(twoq_circ)
noisy_circuit = twoq_circ.with_noise(depolarize(BASE_NOISE))
noisy_choi = _circuit_to_choi(noisy_circuit)
choi_unbiased_estimates = []
for _ in range(500):
imp_circuit, sign, norm = sample_circuit(twoq_circ, decomposition_dict)
noisy_imp_circuit = imp_circuit.with_noise(depolarize(BASE_NOISE))
imp_circuit_choi = _circuit_to_choi(noisy_imp_circuit)
choi_unbiased_estimates.append(norm * sign * imp_circuit_choi)
choi_pec_estimate = np.average(choi_unbiased_estimates, axis=0)
noise_error = np.linalg.norm(ideal_choi - noisy_choi)
pec_error = np.linalg.norm(ideal_choi - choi_pec_estimate)
assert pec_error < noise_error
assert np.allclose(ideal_choi, choi_pec_estimate, atol=0.05)
def test_sample_circuit_types():
imp_circuit, sign, norm = sample_circuit(twoq_circ, DECO_DICT)
assert isinstance(imp_circuit, Circuit)
assert sign in {1, -1}
assert norm > 1
def test_sample_circuit_types_trivial():
imp_circuit, sign, norm = sample_circuit(twoq_circ, NOISELESS_DECO_DICT)
assert imp_circuit == twoq_circ
assert sign == 1
assert np.isclose(norm, 1)
def execute_with_pec(
circuit: QPROGRAM,
executor: Callable[[QPROGRAM], float],
decomposition_dict: DecompositionDict,
precision: float = 0.03,
num_samples: Optional[int] = None,
random_state: Optional[Union[int, np.random.RandomState]] = None,
full_output: bool = False,
) -> Union[float, Tuple[float, float]]:
"""Evaluates the expectation value associated to the input circuit
using probabilistic error cancellation (PEC) [Temme2017]_ [Endo2018]_.
This function implements PEC by:
1. Sampling different implementable circuits from the quasi-probability
representation of the input circuit;
2. Evaluating the noisy expectation values associated to the sampled
circuits (through the "executor" function provided by the user);
3. Estimating the ideal expectation value from a suitable linear
combination of the noisy ones.
Args:
circuit: The input circuit to execute with error-mitigation.
executor: A function which executes a circuit and returns an
expectation value.
decomposition_dict: The decomposition dictionary containing the
quasi-probability representation of the ideal operations (those
which are part of the input circuit).
num_samples: The number of noisy circuits to be sampled for PEC.
If not given, this is deduced from the argument 'precision'.
precision: The desired estimation precision (assuming the observable
is bounded by 1). The number of samples is deduced according
to the formula (one_norm / precision) ** 2, where 'one_norm'
is related to the negativity of the quasi-probability
representation [Temme2017]_. If 'num_samples' is explicitly set
by the user, 'precision' is ignored and has no effect.
random_state: Seed for sampling circuits.
full_output: If False only the average PEC value is returned.
If True an estimate of the associated error is returned too.
Returns:
pec_value: The PEC estimate of the ideal expectation value associated
to the input circuit.
pec_error: The estimated error between the mitigated 'pec_value' and
the actual ideal expectation value. This is estimated as the ratio
pec_std / sqrt(num_samples), where 'pec_std' is the
standard deviation of the PEC samples, i.e., the square root of
the mean squared deviation of the sampled values from 'pec_value'.
This is returned only if 'full_output' is True.
.. [Temme2017] : Kristan Temme, Sergey Bravyi, Jay M. Gambetta,
"Error mitigation for short-depth quantum circuits,"
*Phys. Rev. Lett.* **119**, 180509 (2017),
(https://arxiv.org/abs/1612.02058).
.. [Endo2018] : Suguru Endo, Simon C. Benjamin, Ying Li,
"Practical Quantum Error Mitigation for Near-Future Applications"
*Phys. Rev. **X 8**, 031027 (2018),
(https://arxiv.org/abs/1712.09271).
.. [Takagi2020] : Ryuji Takagi,
"Optimal resource cost for error mitigation,"
(https://arxiv.org/abs/2006.12509).
"""
if isinstance(random_state, int):
random_state = np.random.RandomState(random_state)
# Get the 1-norm of the circuit quasi-probability representation
_, _, norm = sample_circuit(circuit, decomposition_dict)
if not (0 < precision <= 1):
raise ValueError(
"The value of 'precision' should be within the interval (0, 1],"
f" but precision is {precision}."
)
# Deduce the number of samples (if not given by the user)
if not isinstance(num_samples, int):
num_samples = int((norm / precision) ** 2)
# Issue warning for very large sample size
if num_samples > 10 ** 5:
warnings.warn(_LARGE_SAMPLE_WARN, LargeSampleWarning)
sampled_circuits = []
signs = []
for _ in range(num_samples):
sampled_circuit, sign, _ = sample_circuit(
circuit, decomposition_dict, random_state
)
sampled_circuits.append(sampled_circuit)
signs.append(sign)
# TODO gh-412: Add support for batched executors in the PEC module
# Execute all the circuits
exp_values = [executor(circ) for circ in sampled_circuits]
# Evaluate unbiased estimators [Temme2017] [Endo2018] [Takagi2020]
unbiased_estimators = [norm * s * val for s, val in zip(signs, exp_values)]
pec_value = np.average(unbiased_estimators)
if full_output:
pec_error = np.std(unbiased_estimators) / np.sqrt(num_samples)
return pec_value, pec_error
return pec_value
def execute_with_pec(
circuit: QPROGRAM,
executor: Callable[[QPROGRAM], float],
decomposition_dict: DecompositionDict,
num_samples: Optional[int] = None,
random_state: Optional[Union[int, np.random.RandomState]] = None,
full_output: bool = False,
) -> Union[float, Tuple[float, float]]:
"""Evaluates the expectation value associated to the input circuit
using probabilistic error cancellation (PEC) [Temme2017]_.
This function implements PEC by:
1. Sampling different implementable circuits from the quasi-probability
representation of the input circuit;
2. Evaluating the noisy expectation values associated to the sampled
circuits (through the "executor" function provided by the user);
3. Estimating the ideal expectation value from a suitable linear
combination of the noisy ones.
Args:
circuit: The input circuit to execute with error-mitigation.
executor: A function which executes a circuit and returns an
expectation value.
decomposition_dict: The decomposition dictionary containing the
quasi-probability representation of the ideal operations (those
which are part of the input circuit).
num_samples: The number of noisy circuits to be sampled for PEC.
If equal to None, it is deduced from the amount of "negativity"
of the quasi-probability representation of the input circuit.
Note: the latter feature is not yet implemented and num_samples
is just set to 1000 if not specified.
random_state: Seed for sampling circuits.
full_output: If False only the average PEC value is returned.
If True an estimate of the associated error is returned too.
Returns:
pec_value: The PEC estimate of the ideal expectation value associated
to the input circuit.
pec_error: The estimated error between the mitigated 'pec_value' and
the actual ideal expectation value. This is estimated as the ratio
pec_std / sqrt(num_samples), where 'pec_std' is the
standard deviation of the PEC samples, i.e., the square root of
the mean squared deviation of the sampled values from 'pec_value'.
This is returned only if 'full_output' is True.
.. [Temme2017] : Kristan Temme, Sergey Bravyi, Jay M. Gambetta,
"Error mitigation for short-depth quantum circuits,"
*Phys. Rev. Lett.* **119**, 180509 (2017),
(https://arxiv.org/abs/1612.02058).
.. [Endo2018] : Suguru Endo, Simon C. Benjamin, Ying Li,
"Practical Quantum Error Mitigation for Near-Future Applications"
*Phys. Rev. **X 8**, 031027 (2018),
(https://arxiv.org/abs/1712.09271).
.. [Takagi2020] : Ryuji Takagi,
"Optimal resource cost for error mitigation,"
(https://arxiv.org/abs/2006.12509).
"""
# TODO gh-413: Add option to automatically deduce the number of PEC samples
if not num_samples:
num_samples = 1000
sampled_circuits = []
signs = []
for _ in range(num_samples):
# Note: the norm is the same for each sample.
sampled_circuit, sign, norm = sample_circuit(
circuit, decomposition_dict, random_state
)
sampled_circuits.append(sampled_circuit)
signs.append(sign)
# TODO gh-412: Add support for batched executors in the PEC module
# Execute all the circuits
exp_values = [executor(circ) for circ in sampled_circuits]
# Evaluate unbiased estimators [Temme2017], [Endo2018], [Takagi2020]
unbiased_estimators = [norm * s * val for s, val in zip(signs, exp_values)]
pec_value = np.average(unbiased_estimators)
if full_output:
pec_error = np.std(unbiased_estimators) / np.sqrt(num_samples)
return pec_value, pec_error
return pec_value
