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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.","","\"\"\"","DensityMatrix quantum state class.","\"\"\"","","from __future__ import annotations","import copy","from numbers import Number","import numpy as np","","from qiskit.circuit.quantumcircuit import QuantumCircuit","from qiskit.circuit.instruction import Instruction","from qiskit.exceptions import QiskitError","from qiskit.quantum_info.states.quantum_state import QuantumState","from qiskit.quantum_info.operators.mixins.tolerances import TolerancesMixin","from qiskit.quantum_info.operators.op_shape import OpShape","from qiskit.quantum_info.operators.operator import Operator","from qiskit.quantum_info.operators.symplectic import Pauli, SparsePauliOp","from qiskit.quantum_info.operators.scalar_op import ScalarOp","from qiskit.quantum_info.operators.predicates import is_hermitian_matrix","from qiskit.quantum_info.operators.predicates import is_positive_semidefinite_matrix","from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel","from qiskit.quantum_info.operators.channel.superop import SuperOp","","from qiskit._accelerate.pauli_expval import density_expval_pauli_no_x, density_expval_pauli_with_x","from qiskit.quantum_info.states.statevector import Statevector","","","class DensityMatrix(QuantumState, TolerancesMixin):"," \"\"\"DensityMatrix class\"\"\"",""," def __init__("," self,"," data: np.ndarray | list | QuantumCircuit | Instruction | QuantumState,"," dims: int | tuple | list | None = None,"," ):"," \"\"\"Initialize a density matrix object.",""," Args:"," data (np.ndarray or list or matrix_like or QuantumCircuit or"," qiskit.circuit.Instruction):"," A statevector, quantum instruction or an object with a ``to_operator`` or"," ``to_matrix`` method from which the density matrix can be constructed."," If a vector the density matrix is constructed as the projector of that vector."," If a quantum instruction, the density matrix is constructed by assuming all"," qubits are initialized in the zero state."," dims (int or tuple or list): Optional. The subsystem dimension"," of the state (See additional information).",""," Raises:"," QiskitError: if input data is not valid.",""," Additional Information:"," The ``dims`` kwarg can be None, an integer, or an iterable of"," integers.",""," * ``Iterable`` -- the subsystem dimensions are the values in the list"," with the total number of subsystems given by the length of the list.",""," * ``Int`` or ``None`` -- the leading dimension of the input matrix"," specifies the total dimension of the density matrix. If it is a"," power of two the state will be initialized as an N-qubit state."," If it is not a power of two the state will have a single"," d-dimensional subsystem."," \"\"\""," if isinstance(data, (list, np.ndarray)):"," # Finally we check if the input is a raw matrix in either a"," # python list or numpy array format."," self._data = np.asarray(data, dtype=complex)"," elif isinstance(data, (QuantumCircuit, Instruction)):"," # If the data is a circuit or an instruction use the classmethod"," # to construct the DensityMatrix object"," self._data = DensityMatrix.from_instruction(data)._data"," elif hasattr(data, \"to_operator\"):"," # If the data object has a 'to_operator' attribute this is given"," # higher preference than the 'to_matrix' method for initializing"," # an Operator object."," op = data.to_operator()"," self._data = op.data"," if dims is None:"," dims = op.output_dims()"," elif hasattr(data, \"to_matrix\"):"," # If no 'to_operator' attribute exists we next look for a"," # 'to_matrix' attribute to a matrix that will be cast into"," # a complex numpy matrix."," self._data = np.asarray(data.to_matrix(), dtype=complex)"," else:"," raise QiskitError(\"Invalid input data format for DensityMatrix\")"," # Convert statevector into a density matrix"," ndim = self._data.ndim"," shape = self._data.shape"," if ndim == 2 and shape[0] == shape[1]:"," pass # We good"," elif ndim == 1:"," self._data = np.outer(self._data, np.conj(self._data))"," elif ndim == 2 and shape[1] == 1:"," self._data = np.reshape(self._data, shape[0])"," else:"," raise QiskitError(\"Invalid DensityMatrix input: not a square matrix.\")"," super().__init__(op_shape=OpShape.auto(shape=self._data.shape, dims_l=dims, dims_r=dims))",""," def __array__(self, dtype=None):"," if dtype:"," return np.asarray(self.data, dtype=dtype)"," return self.data",""," def __eq__(self, other):"," return super().__eq__(other) and np.allclose("," self._data, other._data, rtol=self.rtol, atol=self.atol"," )",""," def __repr__(self):"," prefix = \"DensityMatrix(\""," pad = len(prefix) * \" \""," return \"{}{},\\n{}dims={})\".format("," prefix,"," np.array2string(self._data, separator=\", \", prefix=prefix),"," pad,"," self._op_shape.dims_l(),"," )",""," @property"," def settings(self):"," \"\"\"Return settings.\"\"\""," return {\"data\": self.data, \"dims\": self._op_shape.dims_l()}",""," def draw(self, output: str | None = None, **drawer_args):"," \"\"\"Return a visualization of the Statevector.",""," **repr**: ASCII TextMatrix of the state's ``__repr__``.",""," **text**: ASCII TextMatrix that can be printed in the console.",""," **latex**: An IPython Latex object for displaying in Jupyter Notebooks.",""," **latex_source**: Raw, uncompiled ASCII source to generate array using LaTeX.",""," **qsphere**: Matplotlib figure, rendering of density matrix using `plot_state_qsphere()`.",""," **hinton**: Matplotlib figure, rendering of density matrix using `plot_state_hinton()`.",""," **bloch**: Matplotlib figure, rendering of density matrix using `plot_bloch_multivector()`.",""," Args:"," output (str): Select the output method to use for drawing the"," state. Valid choices are `repr`, `text`, `latex`, `latex_source`,"," `qsphere`, `hinton`, or `bloch`. Default is `repr`. Default can"," be changed by adding the line ``state_drawer = `` to"," ``~/.qiskit/settings.conf`` under ``[default]``."," drawer_args: Arguments to be passed directly to the relevant drawing"," function or constructor (`TextMatrix()`, `array_to_latex()`,"," `plot_state_qsphere()`, `plot_state_hinton()` or `plot_bloch_multivector()`)."," See the relevant function under `qiskit.visualization` for that function's"," documentation.",""," Returns:"," :class:`matplotlib.Figure` or :class:`str` or"," :class:`TextMatrix` or :class:`IPython.display.Latex`:"," Drawing of the Statevector.",""," Raises:"," ValueError: when an invalid output method is selected."," \"\"\""," # pylint: disable=cyclic-import"," from qiskit.visualization.state_visualization import state_drawer",""," return state_drawer(self, output=output, **drawer_args)",""," def _ipython_display_(self):"," out = self.draw()"," if isinstance(out, str):"," print(out)"," else:"," from IPython.display import display",""," display(out)",""," @property"," def data(self):"," \"\"\"Return data.\"\"\""," return self._data",""," def is_valid(self, atol=None, rtol=None):"," \"\"\"Return True if trace 1 and positive semidefinite.\"\"\""," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol"," # Check trace == 1"," if not np.allclose(self.trace(), 1, rtol=rtol, atol=atol):"," return False"," # Check Hermitian"," if not is_hermitian_matrix(self.data, rtol=rtol, atol=atol):"," return False"," # Check positive semidefinite"," return is_positive_semidefinite_matrix(self.data, rtol=rtol, atol=atol)",""," def to_operator(self) -> Operator:"," \"\"\"Convert to Operator\"\"\""," dims = self.dims()"," return Operator(self.data, input_dims=dims, output_dims=dims)",""," def conjugate(self):"," \"\"\"Return the conjugate of the density matrix.\"\"\""," return DensityMatrix(np.conj(self.data), dims=self.dims())",""," def trace(self):"," \"\"\"Return the trace of the density matrix.\"\"\""," return np.trace(self.data)",""," def purity(self):"," \"\"\"Return the purity of the quantum state.\"\"\""," # For a valid statevector the purity is always 1, however if we simply"," # have an arbitrary vector (not correctly normalized) then the"," # purity is equivalent to the trace squared:"," # P(|psi>) = Tr[|psi>|^2"," return np.trace(np.dot(self.data, self.data))",""," def tensor(self, other: DensityMatrix) -> DensityMatrix:"," \"\"\"Return the tensor product state self ⊗ other.",""," Args:"," other (DensityMatrix): a quantum state object.",""," Returns:"," DensityMatrix: the tensor product operator self ⊗ other.",""," Raises:"," QiskitError: if other is not a quantum state."," \"\"\""," if not isinstance(other, DensityMatrix):"," other = DensityMatrix(other)"," ret = copy.copy(self)"," ret._data = np.kron(self._data, other._data)"," ret._op_shape = self._op_shape.tensor(other._op_shape)"," return ret",""," def expand(self, other: DensityMatrix) -> DensityMatrix:"," \"\"\"Return the tensor product state other ⊗ self.",""," Args:"," other (DensityMatrix): a quantum state object.",""," Returns:"," DensityMatrix: the tensor product state other ⊗ self.",""," Raises:"," QiskitError: if other is not a quantum state."," \"\"\""," if not isinstance(other, DensityMatrix):"," other = DensityMatrix(other)"," ret = copy.copy(self)"," ret._data = np.kron(other._data, self._data)"," ret._op_shape = self._op_shape.expand(other._op_shape)"," return ret",""," def _add(self, other):"," \"\"\"Return the linear combination self + other.",""," Args:"," other (DensityMatrix): a quantum state object.",""," Returns:"," DensityMatrix: the linear combination self + other.",""," Raises:"," QiskitError: if other is not a quantum state, or has"," incompatible dimensions."," \"\"\""," if not isinstance(other, DensityMatrix):"," other = DensityMatrix(other)"," self._op_shape._validate_add(other._op_shape)"," ret = copy.copy(self)"," ret._data = self.data + other.data"," return ret",""," def _multiply(self, other):"," \"\"\"Return the scalar multiplied state other * self.",""," Args:"," other (complex): a complex number.",""," Returns:"," DensityMatrix: the scalar multiplied state other * self.",""," Raises:"," QiskitError: if other is not a valid complex number."," \"\"\""," if not isinstance(other, Number):"," raise QiskitError(\"other is not a number\")"," ret = copy.copy(self)"," ret._data = other * self.data"," return ret",""," def evolve("," self,"," other: Operator | QuantumChannel | Instruction | QuantumCircuit,"," qargs: list[int] | None = None,"," ) -> DensityMatrix:"," \"\"\"Evolve a quantum state by an operator.",""," Args:"," other (Operator or QuantumChannel"," or Instruction or Circuit): The operator to evolve by."," qargs (list): a list of QuantumState subsystem positions to apply"," the operator on.",""," Returns:"," DensityMatrix: the output density matrix.",""," Raises:"," QiskitError: if the operator dimension does not match the"," specified QuantumState subsystem dimensions."," \"\"\""," if qargs is None:"," qargs = getattr(other, \"qargs\", None)",""," # Evolution by a circuit or instruction"," if isinstance(other, (QuantumCircuit, Instruction)):"," return self._evolve_instruction(other, qargs=qargs)",""," # Evolution by a QuantumChannel"," # Currently the class that has `to_quantumchannel` is QuantumError of Qiskit Aer, so we can't"," # use QuantumError as a type hint."," if hasattr(other, \"to_quantumchannel\"):"," return other.to_quantumchannel()._evolve(self, qargs=qargs)"," if isinstance(other, QuantumChannel):"," return other._evolve(self, qargs=qargs)",""," # Unitary evolution by an Operator"," if not isinstance(other, Operator):"," dims = self.dims(qargs=qargs)"," other = Operator(other, input_dims=dims, output_dims=dims)"," return self._evolve_operator(other, qargs=qargs)",""," def reverse_qargs(self) -> DensityMatrix:"," r\"\"\"Return a DensityMatrix with reversed subsystem ordering.",""," For a tensor product state this is equivalent to reversing the order"," of tensor product subsystems. For a density matrix"," :math:`\\rho = \\rho_{n-1} \\otimes ... \\otimes \\rho_0`"," the returned state will be"," :math:`\\rho_0 \\otimes ... \\otimes \\rho_{n-1}`.",""," Returns:"," DensityMatrix: the state with reversed subsystem order."," \"\"\""," ret = copy.copy(self)"," axes = tuple(range(self._op_shape._num_qargs_l - 1, -1, -1))"," axes = axes + tuple(len(axes) + i for i in axes)"," ret._data = np.reshape("," np.transpose(np.reshape(self.data, self._op_shape.tensor_shape), axes),"," self._op_shape.shape,"," )"," ret._op_shape = self._op_shape.reverse()"," return ret",""," def _expectation_value_pauli(self, pauli, qargs=None):"," \"\"\"Compute the expectation value of a Pauli.",""," Args:"," pauli (Pauli): a Pauli operator to evaluate expval of."," qargs (None or list): subsystems to apply operator on.",""," Returns:"," complex: the expectation value."," \"\"\""," n_pauli = len(pauli)"," if qargs is None:"," qubits = np.arange(n_pauli)"," else:"," qubits = np.array(qargs)"," x_mask = np.dot(1 << qubits, pauli.x)"," z_mask = np.dot(1 << qubits, pauli.z)"," pauli_phase = (-1j) ** pauli.phase if pauli.phase else 1",""," if x_mask + z_mask == 0:"," return pauli_phase * self.trace()",""," data = np.ravel(self.data, order=\"F\")"," if x_mask == 0:"," return pauli_phase * density_expval_pauli_no_x(data, self.num_qubits, z_mask)",""," x_max = qubits[pauli.x][-1]"," y_phase = (-1j) ** pauli._count_y()"," y_phase = y_phase[0]"," return pauli_phase * density_expval_pauli_with_x("," data, self.num_qubits, z_mask, x_mask, y_phase, x_max"," )",""," def expectation_value(self, oper: Operator, qargs: None | list[int] = None) -> complex:"," \"\"\"Compute the expectation value of an operator.",""," Args:"," oper (Operator): an operator to evaluate expval."," qargs (None or list): subsystems to apply the operator on.",""," Returns:"," complex: the expectation value."," \"\"\""," if isinstance(oper, Pauli):"," return self._expectation_value_pauli(oper, qargs)",""," if isinstance(oper, SparsePauliOp):"," return sum("," coeff * self._expectation_value_pauli(Pauli((z, x)), qargs)"," for z, x, coeff in zip(oper.paulis.z, oper.paulis.x, oper.coeffs)"," )",""," if not isinstance(oper, Operator):"," oper = Operator(oper)"," return np.trace(Operator(self).dot(oper, qargs=qargs).data)",""," def probabilities("," self, qargs: None | list[int] = 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.",""," Examples:",""," Consider a 2-qubit product state :math:`\\\\rho=\\\\rho_1\\\\otimes\\\\rho_0`"," with :math:`\\\\rho_1=|+\\\\rangle\\\\!\\\\langle+|`,"," :math:`\\\\rho_0=|0\\\\rangle\\\\!\\\\langle0|`.",""," .. code-block::",""," from qiskit.quantum_info import DensityMatrix",""," rho = DensityMatrix.from_label('+0')",""," # Probabilities for measuring both qubits"," probs = rho.probabilities()"," print('probs: {}'.format(probs))",""," # Probabilities for measuring only qubit-0"," probs_qubit_0 = rho.probabilities([0])"," print('Qubit-0 probs: {}'.format(probs_qubit_0))",""," # Probabilities for measuring only qubit-1"," probs_qubit_1 = rho.probabilities([1])"," print('Qubit-1 probs: {}'.format(probs_qubit_1))",""," .. parsed-literal::",""," probs: [0.5 0. 0.5 0. ]"," Qubit-0 probs: [1. 0.]"," Qubit-1 probs: [0.5 0.5]",""," We can also permute the order of qubits in the ``qargs`` list"," to change the qubit position in the probabilities output",""," .. code-block::",""," from qiskit.quantum_info import DensityMatrix",""," rho = DensityMatrix.from_label('+0')",""," # Probabilities for measuring both qubits"," probs = rho.probabilities([0, 1])"," print('probs: {}'.format(probs))",""," # Probabilities for measuring both qubits"," # but swapping qubits 0 and 1 in output"," probs_swapped = rho.probabilities([1, 0])"," print('Swapped probs: {}'.format(probs_swapped))",""," .. parsed-literal::",""," probs: [0.5 0. 0.5 0. ]"," Swapped probs: [0.5 0.5 0. 0. ]"," \"\"\""," probs = self._subsystem_probabilities("," np.abs(self.data.diagonal()), self._op_shape.dims_l(), qargs=qargs"," )",""," # to account for roundoff errors, we clip"," probs = np.clip(probs, a_min=0, a_max=1)",""," if decimals is not None:"," probs = probs.round(decimals=decimals)",""," return probs",""," def reset(self, qargs: list[int] | None = None) -> DensityMatrix:"," \"\"\"Reset state or subsystems to the 0-state.",""," Args:"," qargs (list or None): subsystems to reset, if None all"," subsystems will be reset to their 0-state"," (Default: None).",""," Returns:"," DensityMatrix: the reset state.",""," Additional Information:"," If all subsystems are reset this will return the ground state"," on all subsystems. If only a some subsystems are reset this"," function will perform evolution by the reset"," :class:`~qiskit.quantum_info.SuperOp` of the reset subsystems."," \"\"\""," if qargs is None:"," # Resetting all qubits does not require sampling or RNG"," ret = copy.copy(self)"," state = np.zeros(self._op_shape.shape, dtype=complex)"," state[0, 0] = 1"," ret._data = state"," return ret",""," # Reset by evolving by reset SuperOp"," dims = self.dims(qargs)"," reset_superop = SuperOp(ScalarOp(dims, coeff=0))"," reset_superop.data[0] = Operator(ScalarOp(dims)).data.ravel()"," return self.evolve(reset_superop, qargs=qargs)",""," @classmethod"," def from_label(cls, label: str) -> DensityMatrix:"," r\"\"\"Return a tensor product of Pauli X,Y,Z eigenstates.",""," .. list-table:: Single-qubit state labels"," :header-rows: 1",""," * - Label"," - Statevector"," * - ``\"0\"``"," - :math:`\\begin{pmatrix} 1 & 0 \\\\ 0 & 0 \\end{pmatrix}`"," * - ``\"1\"``"," - :math:`\\begin{pmatrix} 0 & 0 \\\\ 0 & 1 \\end{pmatrix}`"," * - ``\"+\"``"," - :math:`\\frac{1}{2}\\begin{pmatrix} 1 & 1 \\\\ 1 & 1 \\end{pmatrix}`"," * - ``\"-\"``"," - :math:`\\frac{1}{2}\\begin{pmatrix} 1 & -1 \\\\ -1 & 1 \\end{pmatrix}`"," * - ``\"r\"``"," - :math:`\\frac{1}{2}\\begin{pmatrix} 1 & -i \\\\ i & 1 \\end{pmatrix}`"," * - ``\"l\"``"," - :math:`\\frac{1}{2}\\begin{pmatrix} 1 & i \\\\ -i & 1 \\end{pmatrix}`",""," Args:"," label (string): a eigenstate string ket label (see table for"," allowed values).",""," Returns:"," DensityMatrix: The N-qubit basis state density matrix.",""," Raises:"," QiskitError: if the label contains invalid characters, or the length"," of the label is larger than an explicitly specified num_qubits."," \"\"\"",""," return DensityMatrix(Statevector.from_label(label))",""," @staticmethod"," def from_int(i: int, dims: int | tuple | list) -> DensityMatrix:"," \"\"\"Return a computational basis state density matrix.",""," Args:"," i (int): the basis state element."," dims (int or tuple or list): The subsystem dimensions of the statevector"," (See additional information).",""," Returns:"," DensityMatrix: The computational basis state :math:`|i\\\\rangle\\\\!\\\\langle i|`.",""," Additional Information:"," The ``dims`` kwarg can be an integer or an iterable of integers.",""," * ``Iterable`` -- the subsystem dimensions are the values in the list"," with the total number of subsystems given by the length of the list.",""," * ``Int`` -- the integer specifies the total dimension of the"," state. If it is a power of two the state will be initialized"," as an N-qubit state. If it is not a power of two the state"," will have a single d-dimensional subsystem."," \"\"\""," size = np.prod(dims)"," state = np.zeros((size, size), dtype=complex)"," state[i, i] = 1.0"," return DensityMatrix(state, dims=dims)",""," @classmethod"," def from_instruction(cls, instruction: Instruction | QuantumCircuit) -> DensityMatrix:"," \"\"\"Return the output density matrix of an instruction.",""," The statevector is initialized in the state :math:`|{0,\\\\ldots,0}\\\\rangle` of"," the same number of qubits as the input instruction or circuit, evolved"," by the input instruction, and the output statevector returned.",""," Args:"," instruction (qiskit.circuit.Instruction or QuantumCircuit): instruction or circuit",""," Returns:"," DensityMatrix: the final density matrix.",""," Raises:"," QiskitError: if the instruction contains invalid instructions for"," density matrix simulation."," \"\"\""," # Convert circuit to an instruction"," if isinstance(instruction, QuantumCircuit):"," instruction = instruction.to_instruction()"," # Initialize an the statevector in the all |0> state"," num_qubits = instruction.num_qubits"," init = np.zeros((2**num_qubits, 2**num_qubits), dtype=complex)"," init[0, 0] = 1"," vec = DensityMatrix(init, dims=num_qubits * (2,))"," vec._append_instruction(instruction)"," return vec",""," def to_dict(self, decimals: None | int = None) -> dict:"," r\"\"\"Convert the density matrix to dictionary form.",""," 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:"," decimals (None or int): the number of decimal places to round"," values. If None no rounding is done"," (Default: None).",""," Returns:"," dict: the dictionary form of the DensityMatrix.",""," Examples:",""," The ket-form of a 2-qubit density matrix"," :math:`rho = |-\\rangle\\!\\langle -|\\otimes |0\\rangle\\!\\langle 0|`",""," .. code-block::",""," from qiskit.quantum_info import DensityMatrix",""," rho = DensityMatrix.from_label('-0')"," print(rho.to_dict())",""," .. parsed-literal::",""," {"," '00|00': (0.4999999999999999+0j),"," '10|00': (-0.4999999999999999-0j),"," '00|10': (-0.4999999999999999+0j),"," '10|10': (0.4999999999999999+0j)"," }",""," For non-qubit subsystems the integer range can go from 0 to 9. For"," example in a qutrit system",""," .. code-block::",""," import numpy as np"," from qiskit.quantum_info import DensityMatrix",""," mat = np.zeros((9, 9))"," mat[0, 0] = 0.25"," mat[3, 3] = 0.25"," mat[6, 6] = 0.25"," mat[-1, -1] = 0.25"," rho = DensityMatrix(mat, dims=(3, 3))"," print(rho.to_dict())",""," .. parsed-literal::",""," {'00|00': (0.25+0j), '10|10': (0.25+0j), '20|20': (0.25+0j), '22|22': (0.25+0j)}",""," For large subsystem dimensions delimiters are required. The"," following example is for a 20-dimensional system consisting of"," a qubit and 10-dimensional qudit.",""," .. code-block::",""," import numpy as np"," from qiskit.quantum_info import DensityMatrix",""," mat = np.zeros((2 * 10, 2 * 10))"," mat[0, 0] = 0.5"," mat[-1, -1] = 0.5"," rho = DensityMatrix(mat, dims=(2, 10))"," print(rho.to_dict())",""," .. parsed-literal::",""," {'00|00': (0.5+0j), '91|91': (0.5+0j)}"," \"\"\""," return self._matrix_to_dict("," self.data, self._op_shape.dims_l(), decimals=decimals, string_labels=True"," )",""," def _evolve_operator(self, other, qargs=None):"," \"\"\"Evolve density matrix by an operator\"\"\""," # Get shape of output density matrix"," new_shape = self._op_shape.compose(other._op_shape, qargs=qargs)"," new_shape._dims_r = new_shape._dims_l"," new_shape._num_qargs_r = new_shape._num_qargs_l",""," ret = copy.copy(self)"," if qargs is None:"," # Evolution on full matrix"," op_mat = other.data"," ret._data = np.dot(op_mat, self.data).dot(op_mat.T.conj())"," ret._op_shape = new_shape"," return ret",""," # Reshape statevector and operator"," tensor = np.reshape(self.data, self._op_shape.tensor_shape)"," # Construct list of tensor indices of statevector to be contracted"," num_indices = len(self.dims())"," indices = [num_indices - 1 - qubit for qubit in qargs]"," # Left multiple by mat"," mat = np.reshape(other.data, other._op_shape.tensor_shape)"," tensor = Operator._einsum_matmul(tensor, mat, indices)"," # Right multiply by mat ** dagger"," adj = other.adjoint()"," mat_adj = np.reshape(adj.data, adj._op_shape.tensor_shape)"," tensor = Operator._einsum_matmul(tensor, mat_adj, indices, num_indices, True)"," # Replace evolved dimensions"," ret._data = np.reshape(tensor, new_shape.shape)"," ret._op_shape = new_shape"," return ret",""," def _append_instruction(self, other, qargs=None):"," \"\"\"Update the current Statevector by applying an instruction.\"\"\""," from qiskit.circuit.reset import Reset"," from qiskit.circuit.barrier import Barrier",""," # Try evolving by a matrix operator (unitary-like evolution)"," mat = Operator._instruction_to_matrix(other)"," if mat is not None:"," self._data = self._evolve_operator(Operator(mat), qargs=qargs).data"," return",""," # Special instruction types"," if isinstance(other, Reset):"," self._data = self.reset(qargs)._data"," return"," if isinstance(other, Barrier):"," return",""," # Otherwise try evolving by a Superoperator"," chan = SuperOp._instruction_to_superop(other)"," if chan is not None:"," # Evolve current state by the superoperator"," self._data = chan._evolve(self, qargs=qargs).data"," return"," # If the instruction doesn't have a matrix defined we use its"," # circuit decomposition definition if it exists, otherwise we"," # cannot compose this gate and raise an error."," if other.definition is None:"," raise QiskitError(f\"Cannot apply Instruction: {other.name}\")"," if not isinstance(other.definition, QuantumCircuit):"," raise QiskitError("," \"{} instruction definition is {}; expected QuantumCircuit\".format("," other.name, type(other.definition)"," )"," )"," qubit_indices = {bit: idx for idx, bit in enumerate(other.definition.qubits)}"," for instruction in other.definition:"," if instruction.clbits:"," raise QiskitError("," f\"Cannot apply instruction with classical bits: {instruction.operation.name}\""," )"," # Get the integer position of the flat register"," if qargs is None:"," new_qargs = [qubit_indices[tup] for tup in instruction.qubits]"," else:"," new_qargs = [qargs[qubit_indices[tup]] for tup in instruction.qubits]"," self._append_instruction(instruction.operation, qargs=new_qargs)",""," def _evolve_instruction(self, obj, qargs=None):"," \"\"\"Return a new statevector by applying an instruction.\"\"\""," if isinstance(obj, QuantumCircuit):"," obj = obj.to_instruction()"," vec = copy.copy(self)"," vec._append_instruction(obj, qargs=qargs)"," return vec",""," def to_statevector(self, atol: float | None = None, rtol: float | None = None) -> Statevector:"," \"\"\"Return a statevector from a pure density matrix.",""," Args:"," atol (float): Absolute tolerance for checking operation validity."," rtol (float): Relative tolerance for checking operation validity.",""," Returns:"," Statevector: The pure density matrix's corresponding statevector."," Corresponds to the eigenvector of the only non-zero eigenvalue.",""," Raises:"," QiskitError: if the state is not pure."," \"\"\"",""," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol",""," if not is_hermitian_matrix(self._data, atol=atol, rtol=rtol):"," raise QiskitError(\"Not a valid density matrix (non-hermitian).\")",""," evals, evecs = np.linalg.eig(self._data)",""," nonzero_evals = evals[abs(evals) > atol]"," if len(nonzero_evals) != 1 or not np.isclose(nonzero_evals[0], 1, atol=atol, rtol=rtol):"," raise QiskitError(\"Density matrix is not a pure state\")",""," psi = evecs[:, np.argmax(evals)] # eigenvectors returned in columns."," return Statevector(psi)",""," def partial_transpose(self, qargs: list[int]) -> DensityMatrix:"," \"\"\"Return partially transposed density matrix.",""," Args:"," qargs (list): The subsystems to be transposed.",""," Returns:"," DensityMatrix: The partially transposed density matrix."," \"\"\""," arr = self._data.reshape(self._op_shape.tensor_shape)"," qargs = len(self._op_shape.dims_l()) - 1 - np.array(qargs)"," n = len(self.dims())"," lst = list(range(2 * n))"," for i in qargs:"," lst[i], lst[i + n] = lst[i + n], lst[i]"," rho = np.transpose(arr, lst)"," rho = np.reshape(rho, self._op_shape.shape)"," return DensityMatrix(rho, 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