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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.","","\"\"\"","Statevector quantum state class.","\"\"\"","from __future__ import annotations","import copy","import re","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.operator import Operator, BaseOperator","from qiskit.quantum_info.operators.symplectic import Pauli, SparsePauliOp","from qiskit.quantum_info.operators.op_shape import OpShape","from qiskit.quantum_info.operators.predicates import matrix_equal","","from qiskit._accelerate.pauli_expval import ("," expval_pauli_no_x,"," expval_pauli_with_x,",")","","","class Statevector(QuantumState, TolerancesMixin):"," \"\"\"Statevector class\"\"\"",""," def __init__("," self,"," data: np.ndarray | list | Statevector | Operator | QuantumCircuit | Instruction,"," dims: int | tuple | list | None = None,"," ):"," \"\"\"Initialize a statevector object.",""," Args:"," data (np.array or list or Statevector or Operator or QuantumCircuit or"," qiskit.circuit.Instruction):"," Data from which the statevector can be constructed. This can be either a complex"," vector, another statevector, a ``Operator`` with only one column or a"," ``QuantumCircuit`` or ``Instruction``. If the data is a circuit or instruction,"," the statevector is constructed by assuming that all qubits are initialized to 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 length of the input vector"," 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 vector in either a"," # python list or numpy array format."," self._data = np.asarray(data, dtype=complex)"," elif isinstance(data, Statevector):"," self._data = data._data"," if dims is None:"," dims = data._op_shape._dims_l"," elif isinstance(data, Operator):"," # We allow conversion of column-vector operators to Statevectors"," input_dim, _ = data.dim"," if input_dim != 1:"," raise QiskitError(\"Input Operator is not a column-vector.\")"," self._data = np.ravel(data.data)"," elif isinstance(data, (QuantumCircuit, Instruction)):"," self._data = Statevector.from_instruction(data).data"," else:"," raise QiskitError(\"Invalid input data format for Statevector\")"," # Check that the input is a numpy vector or column-vector numpy"," # matrix. If it is a column-vector matrix reshape to a vector."," ndim = self._data.ndim"," shape = self._data.shape"," if ndim != 1:"," if ndim == 2 and shape[1] == 1:"," self._data = np.reshape(self._data, shape[0])"," shape = self._data.shape"," elif ndim != 2 or shape[1] != 1:"," raise QiskitError(\"Invalid input: not a vector or column-vector.\")"," super().__init__(op_shape=OpShape.auto(shape=shape, dims_l=dims, num_qubits_r=0))",""," 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 = \"Statevector(\""," 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) -> dict:"," \"\"\"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 statevector using `plot_state_qsphere()`.",""," **hinton**: Matplotlib figure, rendering of statevector using `plot_state_hinton()`.",""," **bloch**: Matplotlib figure, rendering of statevector using `plot_bloch_multivector()`.",""," **city**: Matplotlib figure, rendering of statevector using `plot_state_city()`.",""," **paulivec**: Matplotlib figure, rendering of statevector using `plot_state_paulivec()`.",""," Args:"," output (str): Select the output method to use for drawing the"," state. Valid choices are `repr`, `text`, `latex`, `latex_source`,"," `qsphere`, `hinton`, `bloch`, `city`, or `paulivec`. 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.",""," Examples:",""," Plot one of the Bell states",""," .. plot::"," :include-source:",""," from numpy import sqrt"," from qiskit.quantum_info import Statevector"," sv=Statevector([1/sqrt(2), 0, 0, -1/sqrt(2)])"," sv.draw(output='hinton')",""," \"\"\""," # 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)",""," def __getitem__(self, key: int | str) -> np.complex128:"," \"\"\"Return Statevector item either by index or binary label"," Args:"," key (int or str): index or corresponding binary label, e.g. '01' = 1.",""," Returns:"," numpy.complex128: Statevector item.",""," Raises:"," QiskitError: if key is not valid."," \"\"\""," if isinstance(key, str):"," try:"," key = int(key, 2)"," except ValueError:"," raise QiskitError(f\"Key '{key}' is not a valid binary string.\") from None"," if isinstance(key, int):"," if key >= self.dim:"," raise QiskitError(f\"Key {key} is greater than Statevector dimension {self.dim}.\")"," if key < 0:"," raise QiskitError(f\"Key {key} is not a valid positive value.\")"," return self._data[key]"," else:"," raise QiskitError(\"Key must be int or a valid binary string.\")",""," def __iter__(self):"," yield from self._data",""," def __len__(self):"," return len(self._data)",""," @property"," def data(self) -> np.ndarray:"," \"\"\"Return data.\"\"\""," return self._data",""," def is_valid(self, atol: float | None = None, rtol: float | None = None) -> bool:"," \"\"\"Return True if a Statevector has norm 1.\"\"\""," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol"," norm = np.linalg.norm(self.data)"," return np.allclose(norm, 1, rtol=rtol, atol=atol)",""," def to_operator(self) -> Operator:"," \"\"\"Convert state to a rank-1 projector operator\"\"\""," mat = np.outer(self.data, np.conj(self.data))"," return Operator(mat, input_dims=self.dims(), output_dims=self.dims())",""," def conjugate(self) -> Statevector:"," \"\"\"Return the conjugate of the operator.\"\"\""," return Statevector(np.conj(self.data), dims=self.dims())",""," def trace(self) -> np.float64:"," \"\"\"Return the trace of the quantum state as a density matrix.\"\"\""," return np.sum(np.abs(self.data) ** 2)",""," def purity(self) -> np.float64:"," \"\"\"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 self.trace() ** 2",""," def tensor(self, other: Statevector) -> Statevector:"," \"\"\"Return the tensor product state self ⊗ other.",""," Args:"," other (Statevector): a quantum state object.",""," Returns:"," Statevector: the tensor product operator self ⊗ other.",""," Raises:"," QiskitError: if other is not a quantum state."," \"\"\""," if not isinstance(other, Statevector):"," other = Statevector(other)"," ret = copy.copy(self)"," ret._op_shape = self._op_shape.tensor(other._op_shape)"," ret._data = np.kron(self._data, other._data)"," return ret",""," def inner(self, other: Statevector) -> np.complex128:"," r\"\"\"Return the inner product of self and other as"," :math:`\\langle self| other \\rangle`.",""," Args:"," other (Statevector): a quantum state object.",""," Returns:"," np.complex128: the inner product of self and other, :math:`\\langle self| other \\rangle`.",""," Raises:"," QiskitError: if other is not a quantum state or has different dimension."," \"\"\""," if not isinstance(other, Statevector):"," other = Statevector(other)"," if self.dims() != other.dims():"," raise QiskitError("," f\"Statevector dimensions do not match: {self.dims()} and {other.dims()}.\""," )"," inner = np.vdot(self.data, other.data)"," return inner",""," def expand(self, other: Statevector) -> Statevector:"," \"\"\"Return the tensor product state other ⊗ self.",""," Args:"," other (Statevector): a quantum state object.",""," Returns:"," Statevector: the tensor product state other ⊗ self.",""," Raises:"," QiskitError: if other is not a quantum state."," \"\"\""," if not isinstance(other, Statevector):"," other = Statevector(other)"," ret = copy.copy(self)"," ret._op_shape = self._op_shape.expand(other._op_shape)"," ret._data = np.kron(other._data, self._data)"," return ret",""," def _add(self, other):"," \"\"\"Return the linear combination self + other.",""," Args:"," other (Statevector): a quantum state object.",""," Returns:"," Statevector: the linear combination self + other.",""," Raises:"," QiskitError: if other is not a quantum state, or has"," incompatible dimensions."," \"\"\""," if not isinstance(other, Statevector):"," other = Statevector(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 self * other.",""," Args:"," other (complex): a complex number.",""," Returns:"," Statevector: 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 | QuantumCircuit | Instruction, qargs: list[int] | None = None"," ) -> Statevector:"," \"\"\"Evolve a quantum state by the operator.",""," Args:"," other (Operator | QuantumCircuit | circuit.Instruction): The operator to evolve by."," qargs (list): a list of Statevector subsystem positions to apply"," the operator on.",""," Returns:"," Statevector: the output quantum state.",""," Raises:"," QiskitError: if the operator dimension does not match the"," specified Statevector subsystem dimensions."," \"\"\""," if qargs is None:"," qargs = getattr(other, \"qargs\", None)",""," # Get return vector"," ret = copy.copy(self)",""," # Evolution by a circuit or instruction"," if isinstance(other, QuantumCircuit):"," other = other.to_instruction()"," if isinstance(other, Instruction):"," if self.num_qubits is None:"," raise QiskitError(\"Cannot apply QuantumCircuit to non-qubit Statevector.\")"," return self._evolve_instruction(ret, other, qargs=qargs)",""," # Evolution by an Operator"," if not isinstance(other, Operator):"," dims = self.dims(qargs=qargs)"," other = Operator(other, input_dims=dims, output_dims=dims)",""," # check dimension"," if self.dims(qargs) != other.input_dims():"," raise QiskitError("," \"Operator input dimensions are not equal to statevector subsystem dimensions.\""," )"," return Statevector._evolve_operator(ret, other, qargs=qargs)",""," def equiv("," self, other: Statevector, rtol: float | None = None, atol: float | None = None"," ) -> bool:"," \"\"\"Return True if other is equivalent as a statevector up to global phase.",""," .. note::",""," If other is not a Statevector, but can be used to initialize a statevector object,"," this will check that Statevector(other) is equivalent to the current statevector up"," to global phase.",""," Args:"," other (Statevector): an object from which a ``Statevector`` can be constructed."," rtol (float): relative tolerance value for comparison."," atol (float): absolute tolerance value for comparison.",""," Returns:"," bool: True if statevectors are equivalent up to global phase."," \"\"\""," if not isinstance(other, Statevector):"," try:"," other = Statevector(other)"," except QiskitError:"," return False"," if self.dim != other.dim:"," return False"," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol"," return matrix_equal(self.data, other.data, ignore_phase=True, rtol=rtol, atol=atol)",""," def reverse_qargs(self) -> Statevector:"," r\"\"\"Return a Statevector with reversed subsystem ordering.",""," For a tensor product state this is equivalent to reversing the order"," of tensor product subsystems. For a statevector"," :math:`|\\psi \\rangle = |\\psi_{n-1} \\rangle \\otimes ... \\otimes |\\psi_0 \\rangle`"," the returned statevector will be"," :math:`|\\psi_{0} \\rangle \\otimes ... \\otimes |\\psi_{n-1} \\rangle`.",""," Returns:"," Statevector: the Statevector with reversed subsystem order."," \"\"\""," ret = copy.copy(self)"," axes = tuple(range(self._op_shape._num_qargs_l - 1, -1, -1))"," 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 * np.linalg.norm(self.data)",""," if x_mask == 0:"," return pauli_phase * expval_pauli_no_x(self.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 * expval_pauli_with_x("," self.data, self.num_qubits, z_mask, x_mask, y_phase, x_max"," )",""," def expectation_value("," self, oper: BaseOperator | QuantumCircuit | Instruction, qargs: None | list[int] = None"," ) -> complex:"," \"\"\"Compute the expectation value of an operator.",""," Args:"," oper (Operator): an operator to evaluate expval of."," qargs (None or list): subsystems to apply 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)"," )",""," val = self.evolve(oper, qargs=qargs)"," conj = self.conjugate()"," return np.dot(conj.data, val.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:`|\\\\psi\\\\rangle=|+\\\\rangle\\\\otimes|0\\\\rangle`.",""," .. code-block::",""," from qiskit.quantum_info import Statevector",""," psi = Statevector.from_label('+0')",""," # Probabilities for measuring both qubits"," probs = psi.probabilities()"," print('probs: {}'.format(probs))",""," # Probabilities for measuring only qubit-0"," probs_qubit_0 = psi.probabilities([0])"," print('Qubit-0 probs: {}'.format(probs_qubit_0))",""," # Probabilities for measuring only qubit-1"," probs_qubit_1 = psi.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 Statevector",""," psi = Statevector.from_label('+0')",""," # Probabilities for measuring both qubits"," probs = psi.probabilities([0, 1])"," print('probs: {}'.format(probs))",""," # Probabilities for measuring both qubits"," # but swapping qubits 0 and 1 in output"," probs_swapped = psi.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) ** 2, 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) -> Statevector:"," \"\"\"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:"," Statevector: 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 a measurement on those subsystems and"," evolve the subsystems so that the collapsed post-measurement"," states are rotated to the 0-state. The RNG seed for this"," sampling can be set using the :meth:`seed` method."," \"\"\""," 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] = 1"," ret._data = state"," return ret",""," # Sample a single measurement outcome"," dims = self.dims(qargs)"," probs = self.probabilities(qargs)"," sample = self._rng.choice(len(probs), p=probs, size=1)",""," # Convert to projector for state update"," proj = np.zeros(len(probs), dtype=complex)"," proj[sample] = 1 / np.sqrt(probs[sample])",""," # Rotate outcome to 0"," reset = np.eye(len(probs))"," reset[0, 0] = 0"," reset[sample, sample] = 0"," reset[0, sample] = 1",""," # compose with reset projection"," reset = np.dot(reset, np.diag(proj))"," return self.evolve(Operator(reset, input_dims=dims, output_dims=dims), qargs=qargs)",""," @classmethod"," def from_label(cls, label: str) -> Statevector:"," \"\"\"Return a tensor product of Pauli X,Y,Z eigenstates.",""," .. list-table:: Single-qubit state labels"," :header-rows: 1",""," * - Label"," - Statevector"," * - ``\"0\"``"," - :math:`[1, 0]`"," * - ``\"1\"``"," - :math:`[0, 1]`"," * - ``\"+\"``"," - :math:`[1 / \\\\sqrt{2}, 1 / \\\\sqrt{2}]`"," * - ``\"-\"``"," - :math:`[1 / \\\\sqrt{2}, -1 / \\\\sqrt{2}]`"," * - ``\"r\"``"," - :math:`[1 / \\\\sqrt{2}, i / \\\\sqrt{2}]`"," * - ``\"l\"``"," - :math:`[1 / \\\\sqrt{2}, -i / \\\\sqrt{2}]`",""," Args:"," label (string): a eigenstate string ket label (see table for"," allowed values).",""," Returns:"," Statevector: 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."," \"\"\""," # Check label is valid"," if re.match(r\"^[01rl\\-+]+$\", label) is None:"," raise QiskitError(\"Label contains invalid characters.\")"," # We can prepare Z-eigenstates by converting the computational"," # basis bit-string to an integer and preparing that unit vector"," # However, for X-basis states, we will prepare a Z-eigenstate first"," # then apply Hadamard gates to rotate 0 and 1s to + and -."," z_label = label"," xy_states = False"," if re.match(\"^[01]+$\", label) is None:"," # We have X or Y eigenstates so replace +,r with 0 and"," # -,l with 1 and prepare the corresponding Z state"," xy_states = True"," z_label = z_label.replace(\"+\", \"0\")"," z_label = z_label.replace(\"r\", \"0\")"," z_label = z_label.replace(\"-\", \"1\")"," z_label = z_label.replace(\"l\", \"1\")"," # Initialize Z eigenstate vector"," num_qubits = len(label)"," data = np.zeros(1 << num_qubits, dtype=complex)"," pos = int(z_label, 2)"," data[pos] = 1"," state = Statevector(data)"," if xy_states:"," # Apply hadamards to all qubits in X eigenstates"," x_mat = np.array([[1, 1], [1, -1]], dtype=complex) / np.sqrt(2)"," # Apply S.H to qubits in Y eigenstates"," y_mat = np.dot(np.diag([1, 1j]), x_mat)"," for qubit, char in enumerate(reversed(label)):"," if char in [\"+\", \"-\"]:"," state = state.evolve(x_mat, qargs=[qubit])"," elif char in [\"r\", \"l\"]:"," state = state.evolve(y_mat, qargs=[qubit])"," return state",""," @staticmethod"," def from_int(i: int, dims: int | tuple | list) -> Statevector:"," \"\"\"Return a computational basis statevector.",""," Args:"," i (int): the basis state element."," dims (int or tuple or list): The subsystem dimensions of the statevector"," (See additional information).",""," Returns:"," Statevector: The computational basis state :math:`|i\\\\rangle`.",""," 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, dtype=complex)"," state[i] = 1.0"," return Statevector(state, dims=dims)",""," @classmethod"," def from_instruction(cls, instruction: Instruction | QuantumCircuit) -> Statevector:"," \"\"\"Return the output statevector 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:"," Statevector: The final statevector.",""," Raises:"," QiskitError: if the instruction contains invalid instructions for"," the statevector simulation."," \"\"\""," # Convert circuit to an instruction"," if isinstance(instruction, QuantumCircuit):"," instruction = instruction.to_instruction()"," # Initialize an the statevector in the all |0> state"," init = np.zeros(2**instruction.num_qubits, dtype=complex)"," init[0] = 1.0"," vec = Statevector(init, dims=instruction.num_qubits * (2,))"," return Statevector._evolve_instruction(vec, instruction)",""," def to_dict(self, decimals: None | int = None) -> dict:"," r\"\"\"Convert the statevector 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 Statevector.",""," Example:",""," The ket-form of a 2-qubit statevector"," :math:`|\\psi\\rangle = |-\\rangle\\otimes |0\\rangle`",""," .. code-block::",""," from qiskit.quantum_info import Statevector",""," psi = Statevector.from_label('-0')"," print(psi.to_dict())",""," .. parsed-literal::",""," {'00': (0.7071067811865475+0j), '10': (-0.7071067811865475+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 Statevector",""," vec = np.zeros(9)"," vec[0] = 1 / np.sqrt(2)"," vec[-1] = 1 / np.sqrt(2)"," psi = Statevector(vec, dims=(3, 3))"," print(psi.to_dict())",""," .. parsed-literal::",""," {'00': (0.7071067811865475+0j), '22': (0.7071067811865475+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 Statevector",""," vec = np.zeros(2 * 10)"," vec[0] = 1 / np.sqrt(2)"," vec[-1] = 1 / np.sqrt(2)"," psi = Statevector(vec, dims=(2, 10))"," print(psi.to_dict())",""," .. parsed-literal::",""," {'00': (0.7071067811865475+0j), '91': (0.7071067811865475+0j)}",""," \"\"\""," return self._vector_to_dict("," self.data, self._op_shape.dims_l(), decimals=decimals, string_labels=True"," )",""," @staticmethod"," def _evolve_operator(statevec, oper, qargs=None):"," \"\"\"Evolve a qudit statevector\"\"\""," new_shape = statevec._op_shape.compose(oper._op_shape, qargs=qargs)"," if qargs is None:"," # Full system evolution"," statevec._data = np.dot(oper._data, statevec._data)"," statevec._op_shape = new_shape"," return statevec",""," # Get transpose axes"," num_qargs = statevec._op_shape.num_qargs[0]"," indices = [num_qargs - 1 - i for i in reversed(qargs)]"," axes = indices + [i for i in range(num_qargs) if i not in indices]"," axes_inv = np.argsort(axes).tolist()",""," # Calculate contraction dimensions"," contract_dim = oper._op_shape.shape[1]"," contract_shape = (contract_dim, statevec._op_shape.shape[0] // contract_dim)",""," # Reshape and transpose input array for contraction"," tensor = np.transpose("," np.reshape(statevec.data, statevec._op_shape.tensor_shape),"," axes,"," )"," tensor_shape = tensor.shape",""," # Perform contraction"," tensor = np.reshape("," np.dot(oper.data, np.reshape(tensor, contract_shape)),"," tensor_shape,"," )",""," # Transpose back to original subsystem spec and flatten"," statevec._data = np.reshape(np.transpose(tensor, axes_inv), new_shape.shape[0])",""," # Update dimension"," statevec._op_shape = new_shape"," return statevec",""," @staticmethod"," def _evolve_instruction(statevec, obj, qargs=None):"," \"\"\"Update the current Statevector by applying an instruction.\"\"\""," from qiskit.circuit.reset import Reset"," from qiskit.circuit.barrier import Barrier",""," # pylint complains about a cyclic import since the following Initialize file"," # imports the StatePreparation, which again requires the Statevector (this file),"," # but as this is a local import, it's not actually an issue and can be ignored"," # pylint: disable=cyclic-import"," from qiskit.circuit.library.data_preparation.initializer import Initialize",""," mat = Operator._instruction_to_matrix(obj)"," if mat is not None:"," # Perform the composition and inplace update the current state"," # of the operator"," return Statevector._evolve_operator(statevec, Operator(mat), qargs=qargs)",""," # Special instruction types"," if isinstance(obj, Reset):"," statevec._data = statevec.reset(qargs)._data"," return statevec"," if isinstance(obj, Barrier):"," return statevec"," if isinstance(obj, Initialize):"," # state is initialized to labels in the initialize object"," if all(isinstance(param, str) for param in obj.params):"," initialization = Statevector.from_label(\"\".join(obj.params))._data"," # state is initialized to an integer"," # here we're only checking the length as (1) a length-1 object necessarily means the"," # state is described by an integer (as labels were already covered) and (2) the int"," # was cast to a complex and we cannot do an int typecheck anyways"," elif len(obj.params) == 1:"," state = int(np.real(obj.params[0]))"," initialization = Statevector.from_int(state, (2,) * obj.num_qubits)._data"," # state is initialized to the statevector"," else:"," initialization = np.asarray(obj.params, dtype=complex)",""," if qargs is None:"," statevec._data = initialization"," else:"," # if we act on a subsystem we first need to reset and then apply the"," # state preparation"," statevec._data = statevec.reset(qargs)._data"," mat = np.zeros((2 ** len(qargs), 2 ** len(qargs)), dtype=complex)"," mat[:, 0] = initialization"," statevec = Statevector._evolve_operator(statevec, Operator(mat), qargs=qargs)",""," return statevec",""," # 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 obj.definition is None:"," raise QiskitError(f\"Cannot apply Instruction: {obj.name}\")"," if not isinstance(obj.definition, QuantumCircuit):"," raise QiskitError("," \"{} instruction definition is {}; expected QuantumCircuit\".format("," obj.name, type(obj.definition)"," )"," )",""," if obj.definition.global_phase:"," statevec._data *= np.exp(1j * float(obj.definition.global_phase))"," qubits = {qubit: i for i, qubit in enumerate(obj.definition.qubits)}"," for instruction in obj.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 = 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