# 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 typing import Callable, cast, List, Optional, Set, Union, Any, Iterable

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

from collections import defaultdict
from numbers import Number
from mitiq.observable.pauli import PauliString, PauliStringCollection
from mitiq import MeasurementResult, QuantumResult, QPROGRAM


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]

    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)
    ]
