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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2019.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","","\"\"\"","Abstract QuantumState class.","\"\"\"","","from __future__ import annotations","import copy","from abc import abstractmethod","","import numpy as np","","from qiskit.quantum_info.operators.base_operator import BaseOperator","from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel","from qiskit.quantum_info.operators.op_shape import OpShape","from qiskit.quantum_info.operators.operator import Operator","from qiskit.result.counts import Counts","","","class QuantumState:"," \"\"\"Abstract quantum state base class\"\"\"",""," def __init__(self, op_shape: OpShape | None = None):"," \"\"\"Initialize a QuantumState object.",""," Args:"," op_shape (OpShape): Optional, an OpShape object for state dimensions.",""," .. note::",""," If `op_shape`` is specified it will take precedence over other"," kwargs."," \"\"\""," self._op_shape = op_shape"," # RNG for measure functions"," self._rng_generator = None",""," # Set higher priority than Numpy array and matrix classes"," __array_priority__ = 20",""," def __eq__(self, other):"," return isinstance(other, self.__class__) and self.dims() == other.dims()",""," @property"," def dim(self):"," \"\"\"Return total state dimension.\"\"\""," return self._op_shape.shape[0]",""," @property"," def num_qubits(self):"," \"\"\"Return the number of qubits if a N-qubit state or None otherwise.\"\"\""," return self._op_shape.num_qubits",""," @property"," def _rng(self):"," if self._rng_generator is None:"," return np.random.default_rng()"," return self._rng_generator",""," def dims(self, qargs=None):"," \"\"\"Return tuple of input dimension for specified subsystems.\"\"\""," return self._op_shape.dims_l(qargs)",""," def copy(self):"," \"\"\"Make a copy of current operator.\"\"\""," return copy.deepcopy(self)",""," def seed(self, value=None):"," \"\"\"Set the seed for the quantum state RNG.\"\"\""," if value is None:"," self._rng_generator = None"," elif isinstance(value, np.random.Generator):"," self._rng_generator = value"," else:"," self._rng_generator = np.random.default_rng(value)",""," @abstractmethod"," def is_valid(self, atol=None, rtol=None):"," \"\"\"Return True if a valid quantum state.\"\"\""," pass",""," @abstractmethod"," def to_operator(self):"," \"\"\"Convert state to matrix operator class\"\"\""," pass",""," @abstractmethod"," def conjugate(self):"," \"\"\"Return the conjugate of the operator.\"\"\""," pass",""," @abstractmethod"," def trace(self):"," \"\"\"Return the trace of the quantum state as a density matrix.\"\"\""," pass",""," @abstractmethod"," def purity(self):"," \"\"\"Return the purity of the quantum state.\"\"\""," pass",""," @abstractmethod"," def tensor(self, other: QuantumState) -> QuantumState:"," \"\"\"Return the tensor product state self ⊗ other.",""," Args:"," other (QuantumState): a quantum state object.",""," Returns:"," QuantumState: the tensor product operator self ⊗ other.",""," Raises:"," QiskitError: if other is not a quantum state."," \"\"\""," pass",""," @abstractmethod"," def expand(self, other: QuantumState) -> QuantumState:"," \"\"\"Return the tensor product state other ⊗ self.",""," Args:"," other (QuantumState): a quantum state object.",""," Returns:"," QuantumState: the tensor product state other ⊗ self.",""," Raises:"," QiskitError: if other is not a quantum state."," \"\"\""," pass",""," def _add(self, other):"," \"\"\"Return the linear combination self + other.",""," Args:"," other (QuantumState): a state object.",""," Returns:"," QuantumState: the linear combination self + other.",""," Raises:"," NotImplementedError: if subclass does not support addition."," \"\"\""," raise NotImplementedError(f\"{type(self)} does not support addition\")",""," def _multiply(self, other):"," \"\"\"Return the scalar multipled state other * self.",""," Args:"," other (complex): a complex number.",""," Returns:"," QuantumState: the scalar multipled state other * self.",""," Raises:"," NotImplementedError: if subclass does not support scala"," multiplication."," \"\"\""," raise NotImplementedError(f\"{type(self)} does not support scalar multiplication\")",""," @abstractmethod"," def evolve(self, other: Operator | QuantumChannel, qargs: list | None = None) -> QuantumState:"," \"\"\"Evolve a quantum state by the operator.",""," Args:"," other (Operator or QuantumChannel): The operator to evolve by."," qargs (list): a list of QuantumState subsystem positions to apply"," the operator on.",""," Returns:"," QuantumState: the output quantum state.",""," Raises:"," QiskitError: if the operator dimension does not match the"," specified QuantumState subsystem dimensions."," \"\"\""," pass",""," @abstractmethod"," def expectation_value(self, oper: BaseOperator, qargs: None | list = None) -> complex:"," \"\"\"Compute the expectation value of an operator.",""," Args:"," oper (BaseOperator): an operator to evaluate expval."," qargs (None or list): subsystems to apply the operator on.",""," Returns:"," complex: the expectation value."," \"\"\""," pass",""," @abstractmethod"," def probabilities(self, qargs: None | list = None, decimals: None | int = None) -> np.ndarray:"," \"\"\"Return the subsystem measurement probability vector.",""," Measurement probabilities are with respect to measurement in the"," computation (diagonal) basis.",""," Args:"," qargs (None or list): subsystems to return probabilities for,"," if None return for all subsystems (Default: None)."," decimals (None or int): the number of decimal places to round"," values. If None no rounding is done (Default: None).",""," Returns:"," np.array: The Numpy vector array of probabilities."," \"\"\""," pass",""," def probabilities_dict(self, qargs: None | list = None, decimals: None | int = None) -> dict:"," \"\"\"Return the subsystem measurement probability dictionary.",""," Measurement probabilities are with respect to measurement in the"," computation (diagonal) basis.",""," This dictionary representation uses a Ket-like notation where the"," dictionary keys are qudit strings for the subsystem basis vectors."," If any subsystem has a dimension greater than 10 comma delimiters are"," inserted between integers so that subsystems can be distinguished.",""," Args:"," qargs (None or list): subsystems to return probabilities for,"," if None return for all subsystems (Default: None)."," decimals (None or int): the number of decimal places to round"," values. If None no rounding is done (Default: None).",""," Returns:"," dict: The measurement probabilities in dict (ket) form."," \"\"\""," return self._vector_to_dict("," self.probabilities(qargs=qargs, decimals=decimals),"," self.dims(qargs),"," string_labels=True,"," )",""," def sample_memory(self, shots: int, qargs: None | list = None) -> np.ndarray:"," \"\"\"Sample a list of qubit measurement outcomes in the computational basis.",""," Args:"," shots (int): number of samples to generate."," qargs (None or list): subsystems to sample measurements for,"," if None sample measurement of all"," subsystems (Default: None).",""," Returns:"," np.array: list of sampled counts if the order sampled.",""," Additional Information:",""," This function *samples* measurement outcomes using the measure"," :meth:`probabilities` for the current state and `qargs`. It does"," not actually implement the measurement so the current state is"," not modified.",""," The seed for random number generator used for sampling can be"," set to a fixed value by using the stats :meth:`seed` method."," \"\"\""," # Get measurement probabilities for measured qubits"," probs = self.probabilities(qargs)",""," # Generate list of possible outcome string labels"," labels = self._index_to_ket_array("," np.arange(len(probs)), self.dims(qargs), string_labels=True"," )"," return self._rng.choice(labels, p=probs, size=shots)",""," def sample_counts(self, shots: int, qargs: None | list = None) -> Counts:"," \"\"\"Sample a dict of qubit measurement outcomes in the computational basis.",""," Args:"," shots (int): number of samples to generate."," qargs (None or list): subsystems to sample measurements for,"," if None sample measurement of all"," subsystems (Default: None).",""," Returns:"," Counts: sampled counts dictionary.",""," Additional Information:",""," This function *samples* measurement outcomes using the measure"," :meth:`probabilities` for the current state and `qargs`. It does"," not actually implement the measurement so the current state is"," not modified.",""," The seed for random number generator used for sampling can be"," set to a fixed value by using the stats :meth:`seed` method."," \"\"\""," # Sample list of outcomes"," samples = self.sample_memory(shots, qargs=qargs)",""," # Combine all samples into a counts dictionary"," inds, counts = np.unique(samples, return_counts=True)"," return Counts(zip(inds, counts))",""," def measure(self, qargs: list | None = None) -> tuple:"," \"\"\"Measure subsystems and return outcome and post-measure state.",""," Note that this function uses the QuantumStates internal random"," number generator for sampling the measurement outcome. The RNG"," seed can be set using the :meth:`seed` method.",""," Args:"," qargs (list or None): subsystems to sample measurements for,"," if None sample measurement of all"," subsystems (Default: None).",""," Returns:"," tuple: the pair ``(outcome, state)`` where ``outcome`` is the"," measurement outcome string label, and ``state`` is the"," collapsed post-measurement state for the corresponding"," outcome."," \"\"\""," # Sample a single measurement outcome from probabilities"," dims = self.dims(qargs)"," probs = self.probabilities(qargs)"," sample = self._rng.choice(len(probs), p=probs, size=1)",""," # Format outcome"," outcome = self._index_to_ket_array(sample, self.dims(qargs), string_labels=True)[0]",""," # Convert to projector for state update"," proj = np.zeros(len(probs), dtype=complex)"," proj[sample] = 1 / np.sqrt(probs[sample])",""," # Update state object"," # TODO: implement a more efficient state update method for"," # diagonal matrix multiplication"," ret = self.evolve(Operator(np.diag(proj), input_dims=dims, output_dims=dims), qargs=qargs)",""," return outcome, ret",""," @staticmethod"," def _index_to_ket_array("," inds: np.ndarray, dims: tuple, string_labels: bool = False"," ) -> np.ndarray:"," \"\"\"Convert an index array into a ket array.",""," Args:"," inds (np.array): an integer index array."," dims (tuple): a list of subsystem dimensions."," string_labels (bool): return ket as string if True, otherwise"," return as index array (Default: False).",""," Returns:"," np.array: an array of ket strings if string_label=True, otherwise"," an array of ket lists."," \"\"\""," shifts = [1]"," for dim in dims[:-1]:"," shifts.append(shifts[-1] * dim)"," kets = np.array([(inds // shift) % dim for dim, shift in zip(dims, shifts)])",""," if string_labels:"," max_dim = max(dims)"," char_kets = np.asarray(kets, dtype=np.str_)"," str_kets = char_kets[0]"," for row in char_kets[1:]:"," if max_dim > 10:"," str_kets = np.char.add(\",\", str_kets)"," str_kets = np.char.add(row, str_kets)"," return str_kets.T",""," return kets.T",""," @staticmethod"," def _vector_to_dict(vec, dims, decimals=None, string_labels=False):"," \"\"\"Convert a vector to a ket dictionary.",""," This representation will not show zero values in the output dict.",""," Args:"," vec (array): a Numpy vector array."," dims (tuple): subsystem dimensions."," decimals (None or int): number of decimal places to round to."," (See Numpy.round), if None no rounding"," is done (Default: None)."," string_labels (bool): return ket as string if True, otherwise"," return as index array (Default: False).",""," Returns:"," dict: the vector in dictionary `ket` form."," \"\"\""," # Get indices of non-zero elements"," vals = vec if decimals is None else vec.round(decimals=decimals)"," (inds,) = vals.nonzero()",""," # Convert to ket tuple based on subsystem dimensions"," kets = QuantumState._index_to_ket_array(inds, dims, string_labels=string_labels)",""," # Make dict of tuples"," if string_labels:"," return dict(zip(kets, vec[inds]))",""," return {tuple(ket): val for ket, val in zip(kets, vals[inds])}",""," @staticmethod"," def _matrix_to_dict(mat, dims, decimals=None, string_labels=False):"," \"\"\"Convert a matrix to a ket dictionary.",""," This representation will not show zero values in the output dict.",""," Args:"," mat (array): a Numpy matrix array."," dims (tuple): subsystem dimensions."," decimals (None or int): number of decimal places to round to."," (See Numpy.round), if None no rounding"," is done (Default: None)."," string_labels (bool): return ket as string if True, otherwise"," return as index array (Default: False).",""," Returns:"," dict: the matrix in dictionary `ket` form."," \"\"\""," # Get indices of non-zero elements"," vals = mat if decimals is None else mat.round(decimals=decimals)"," ("," inds_row,"," inds_col,"," ) = vals.nonzero()",""," # Convert to ket tuple based on subsystem dimensions"," bras = QuantumState._index_to_ket_array(inds_row, dims, string_labels=string_labels)"," kets = QuantumState._index_to_ket_array(inds_col, dims, string_labels=string_labels)",""," # Make dict of tuples"," if string_labels:"," return {"," f\"{ket}|{bra}\": val for ket, bra, val in zip(kets, bras, vals[inds_row, inds_col])"," }",""," return {"," (tuple(ket), tuple(bra)): val"," for ket, bra, val in zip(kets, bras, vals[inds_row, inds_col])"," }",""," @staticmethod"," def _subsystem_probabilities("," probs: np.ndarray, dims: tuple, qargs: None | list = None"," ) -> np.ndarray:"," \"\"\"Marginalize a probability vector according to subsystems.",""," Args:"," probs (np.array): a probability vector Numpy array."," dims (tuple): subsystem dimensions."," qargs (None or list): a list of subsystems to return"," marginalized probabilities for. If None return all"," probabilities (Default: None).",""," Returns:"," np.array: the marginalized probability vector flattened"," for the specified qargs."," \"\"\""," if qargs is None:"," return probs"," # Convert qargs to tensor axes"," probs_tens = np.reshape(probs, list(reversed(dims)))"," ndim = probs_tens.ndim"," qargs_axes = [ndim - 1 - i for i in reversed(qargs)]"," # Get sum axis for marginalized subsystems"," sum_axis = tuple(i for i in range(ndim) if i not in qargs_axes)"," if sum_axis:"," probs_tens = np.sum(probs_tens, axis=sum_axis)"," qargs_axes = np.argsort(np.argsort(qargs_axes))"," # Permute probability vector for desired qargs order"," probs_tens = np.transpose(probs_tens, axes=qargs_axes)"," new_probs = np.reshape(probs_tens, (probs_tens.size,))"," return new_probs",""," # Overloads"," def __and__(self, other):"," return self.evolve(other)",""," def __xor__(self, other):"," return self.tensor(other)",""," def __mul__(self, other):"," return self._multiply(other)",""," def __truediv__(self, other):"," return self._multiply(1 / other)",""," def __rmul__(self, other):"," return self.__mul__(other)",""," def __add__(self, other):"," return self._add(other)",""," def __sub__(self, other):"," return self._add(-other)",""," def __neg__(self):"," return 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