Source code for mitiq.pec.sampling

# Copyright (C) 2020 Unitary Fund
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
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"""Tools for sampling from the noisy representations of ideal operations."""

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

import numpy as np

import cirq

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


[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, _ = convert_to_mitiq(ideal_operation) operation_representation = None for representation in representations: if _equal(representation._ideal, ideal, require_qubit_equality=True): 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, [1] * num_samples, 1.0, ) # Sample from this representation. norm = operation_representation.norm sequences = [] signs = [] for _ in range(num_samples): noisy_op, sign, _ = operation_representation.sample(random_state) sequences.append(noisy_op.circuit()) 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(): # Ignore all measurements. if cirq.is_measurement(op): continue 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