# Source code for mitiq.pec.sampling

```# Copyright (C) Unitary Fund
#
# LICENSE file in the root directory of this source tree.

"""Tools for sampling from the noisy representations of ideal operations."""

import warnings
from copy import deepcopy
from typing import List, Optional, Sequence, Tuple, Union

import cirq
import numpy as np

from mitiq import QPROGRAM
from mitiq.interface import convert_from_mitiq, convert_to_mitiq
from mitiq.pec.types import OperationRepresentation
from mitiq.utils import _equal

[docs]def sample_sequence(
ideal_operation: QPROGRAM,
representations: Sequence[OperationRepresentation],
random_state: Optional[Union[int, np.random.RandomState]] = None,
num_samples: int = 1,
) -> Tuple[List[QPROGRAM], List[int], float]:
"""Samples a list of implementable sequences from the quasi-probability
representation of the input ideal operation.
Returns the list of sequences, the corresponding list of signs and the
one-norm of the quasi-probability representation (of the input operation).

For example, if the ideal operation is U with representation U = a A + b B,
then this function returns A with probability :math:`|a| / (|a| + |b|)` and
B with probability :math:`|b| / (|a| + |b|)`. Also returns sign(a)
(sign(b)) and :math:`|a| + |b|` if A (B) is sampled.

Note that the ideal operation can be a sequence of operations (circuit),
for instance U = V W, as long as a representation is known. Similarly, A
and B can be sequences of operations (circuits) or just single operations.

Args:
ideal_operation: The ideal operation from which an implementable
sequence is sampled.
representations: A list of representations of ideal operations in a
noisy basis. If no representation is found for `ideal_operation`,
a ValueError is raised.
random_state: Seed for sampling.
num_samples: The number of samples.

Returns:
The tuple (``sequences``, ``signs``, ``norm``) where
``sequences`` are the sampled sequences,
``signs`` are the signs associated to the sampled ``sequences`` and
``norm`` is the one-norm of the quasi-probability distribution.

Raises:
ValueError: If no representation is found for `ideal_operation`.
"""
# Grab the representation for the given ideal operation.
ideal, native_type = convert_to_mitiq(ideal_operation)
operation_representation = None
for representation in representations:
if _equal(
representation.ideal,
ideal,
require_qubit_equality=representation.is_qubit_dependent,
):
operation_representation = representation
break
if operation_representation is None:
warnings.warn(
UserWarning(f"No representation found for \n\n{ideal_operation}.")
)
return (
[ideal_operation] * num_samples,
 * num_samples,
1.0,
)

# Qubit mapping is necessary for qubit-independent operation reps
qubit_map = dict(
zip(
sorted(operation_representation.ideal.all_qubits()),
sorted(ideal.all_qubits()),
)
)

# Sample from this representation.
norm = operation_representation.norm
sequences = []
signs = []
for _ in range(num_samples):
noisy_op, sign, _ = operation_representation.sample(random_state)
if operation_representation.is_qubit_dependent:
native_circ = noisy_op.native_circuit
else:
cirq_circ = noisy_op.circuit
cirq_circ = cirq_circ.transform_qubits(qubit_map)
native_circ = convert_from_mitiq(cirq_circ, native_type)
sequences.append(native_circ)
signs.append(sign)

return sequences, signs, norm

[docs]def sample_circuit(
ideal_circuit: QPROGRAM,
representations: Sequence[OperationRepresentation],
random_state: Optional[Union[int, np.random.RandomState]] = None,
num_samples: int = 1,
) -> Tuple[List[QPROGRAM], List[int], float]:
"""Samples a list of implementable circuits from the quasi-probability
representation of the input ideal circuit.
Returns the list of circuits, the corresponding list of signs and the
one-norm of the quasi-probability representation (of the full circuit).

Args:
ideal_circuit: The ideal circuit from which an implementable circuit
is sampled.
representations: List of representations of every operation in the
input circuit. If a representation cannot be found for an operation
in the circuit, a ValueError is raised.
random_state: Seed for sampling.
num_samples: The number of samples.

Returns:
The tuple (``sampled_circuits``, ``signs``, ``norm``) where
``sampled_circuits`` are the sampled implementable circuits,
``signs`` are the signs associated to sampled_circuits and
``norm`` is the one-norm of the circuit representation.

Raises:
ValueError:
If a representation is not found for an operation in the circuit.
"""
if isinstance(random_state, int):
random_state = np.random.RandomState(random_state)

# TODO: Likely to cause issues - conversions may introduce gates which are
#  not included in `decompositions`.
ideal, rtype = convert_to_mitiq(ideal_circuit)

# copy and remove all moments
sampled_circuits = [deepcopy(ideal)[0:0] for _ in range(num_samples)]
sampled_signs = [1 for _ in range(num_samples)]
norm = 1.0

for op in ideal.all_operations():
sequences, loc_signs, loc_norm = sample_sequence(
cirq.Circuit(op),
representations,
num_samples=num_samples,
random_state=random_state,
)
norm *= loc_norm
for j in range(num_samples):
sampled_signs[j] *= loc_signs[j]
cirq_seq, _ = convert_to_mitiq(sequences[j])
sampled_circuits[j].append(cirq_seq.all_operations())

native_circuits = [convert_from_mitiq(c, rtype) for c in sampled_circuits]

return native_circuits, sampled_signs, norm
```