Source code for mitiq.observable.observable

# Copyright (C) 2021 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
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <>.

import copy
from typing import Callable, cast, List, Optional, Set

import numpy as np
import numpy.typing as npt
import cirq

from mitiq.observable.pauli import PauliString, PauliStringCollection
from mitiq._typing import MeasurementResult, QuantumResult, QPROGRAM

[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. """ # TODO: Add option to Combine duplicates. E.g. [Z(0, Z(0)] -> [2*Z(0)]. self._paulis = list(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 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) @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, dtype: type = np.complex128, ) -> 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) matrix = np.zeros(shape=(2**n, 2**n), dtype=dtype) for pauli in self._paulis: matrix += pauli.matrix( qubit_indices_to_include=qubit_indices ).astype(dtype=dtype) return 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 cast(float, np.trace(density_matrix @ observable_matrix)) def __str__(self) -> str: return " + ".join(map(str, self._paulis))