# Copyright (C) Unitary Fund
#
# This source code is licensed under the GPL license (v3) found in the
# LICENSE file in the root directory of this source tree.
import copy
from collections import defaultdict
from numbers import Number
from typing import Any, Callable, Iterable, List, Optional, Set, Union, cast
import cirq
import numpy as np
import numpy.typing as npt
from mitiq import QPROGRAM, MeasurementResult, QuantumResult
from mitiq.observable.pauli import PauliString, PauliStringCollection
[docs]class Observable:
"""A quantum observable typically used to compute its mitigated expectation
value.
"""
def __init__(self, *paulis: PauliString) -> None:
"""Initializes an `Observable` with :class:`.PauliString` objects.
Args:
paulis: PauliStrings used to define the observable.
"""
self._paulis = _combine_duplicate_pauli_strings(paulis)
self._groups: List[PauliStringCollection]
self._ngroups: int
self.partition()
@staticmethod
def from_pauli_string_collections(
*pauli_string_collections: PauliStringCollection,
) -> "Observable":
obs = Observable()
obs._groups = list(pauli_string_collections)
obs._ngroups = len(pauli_string_collections)
obs._paulis = [
pauli
for pauli_string_collection in pauli_string_collections
for pauli in pauli_string_collection.elements
]
return obs
@property
def nterms(self) -> int:
return len(self._paulis)
def _qubits(self) -> Set[cirq.Qid]:
"""Returns all qubits acted on by the Observable."""
return {q for pauli in self._paulis for q in pauli._pauli.qubits}
@property
def paulis(self) -> List[PauliString]:
return self._paulis
@property
def qubit_indices(self) -> List[int]:
return [cast(cirq.LineQubit, q).x for q in sorted(self._qubits())]
@property
def nqubits(self) -> int:
return len(self.qubit_indices)
def __mul__(
self, other: Union["Observable", "PauliString", Number]
) -> "Observable":
if isinstance(other, (PauliString, Number)):
return Observable(*[pauli * other for pauli in self._paulis])
elif isinstance(other, Observable):
return Observable(
*[
pauli * other_pauli
for pauli in self._paulis
for other_pauli in other._paulis
]
)
return NotImplemented
def __rmul__(self, other: Union["PauliString", Number]) -> "Observable":
if isinstance(other, (PauliString, Number)):
return Observable(*[other * pauli for pauli in self._paulis])
return NotImplemented
@property
def groups(self) -> List[PauliStringCollection]:
return self._groups
@property
def ngroups(self) -> int:
return self._ngroups
def partition(self, seed: Optional[int] = None) -> None:
rng = np.random.RandomState(seed)
psets: List[PauliStringCollection] = []
paulis = copy.deepcopy(self._paulis)
rng.shuffle(paulis) # type: ignore
while paulis:
pauli = paulis.pop()
added = False
for i, pset in enumerate(psets):
if pset.can_add(pauli):
pset.add(pauli)
added = True
break
if not added:
psets.append(PauliStringCollection(pauli))
self._groups = psets
self._ngroups = len(self._groups)
def measure_in(self, circuit: QPROGRAM) -> List[QPROGRAM]:
return [pset.measure_in(circuit) for pset in self._groups]
[docs] def matrix(
self,
qubit_indices: Optional[List[int]] = None,
) -> npt.NDArray[np.complex64]:
"""Returns the (potentially very large) matrix of the Observable."""
if qubit_indices is None:
qubit_indices = self.qubit_indices
n = len(qubit_indices)
obs_matrix = np.zeros(shape=(2**n, 2**n), dtype=np.complex64)
for pauli in self._paulis:
obs_matrix += pauli.matrix(qubit_indices_to_include=qubit_indices)
return obs_matrix
def expectation(
self, circuit: QPROGRAM, execute: Callable[[QPROGRAM], QuantumResult]
) -> complex:
from mitiq.executor import Executor # Avoid circular import.
return Executor(execute).evaluate(circuit, observable=self)[0]
def _expectation_from_measurements(
self, measurements: List[MeasurementResult]
) -> float:
return sum(
pset._expectation_from_measurements(bitstrings)
for (pset, bitstrings) in zip(self._groups, measurements)
)
def _expectation_from_density_matrix(
self, density_matrix: npt.NDArray[np.complex64]
) -> float:
observable_matrix = self.matrix()
if density_matrix.shape != observable_matrix.shape:
nqubits = int(np.log2(density_matrix.shape[0]))
density_matrix = cirq.partial_trace(
np.reshape(density_matrix, newshape=[2, 2] * nqubits),
keep_indices=self.qubit_indices,
).reshape(observable_matrix.shape)
return np.real_if_close(
np.trace(density_matrix @ observable_matrix)
).item()
def __str__(self) -> str:
return " + ".join(map(str, self._paulis))
def __eq__(self, other: Any) -> bool:
return np.allclose(self.matrix(), other.matrix())
def _combine_duplicate_pauli_strings(
paulis: Iterable[PauliString],
) -> List[PauliString]:
"""Combines duplicate PauliStrings by adding their coefficients.
Discards paulis with zero coefficients.
Returns: deduped list of PauliStrings.
"""
pauli_string_coefficients: defaultdict[PauliString, complex] = defaultdict(
complex
)
for pauli_string in paulis:
cache_key = pauli_string.with_coeff(1)
pauli_string_coefficients[cache_key] += pauli_string.coeff
return [
pauli_string.with_coeff(coeff)
for (pauli_string, coeff) in pauli_string_coefficients.items()
if not np.isclose(coeff, 0.0)
]