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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2020.","#","# 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.","","\"\"\"","ScalarOp class","\"\"\"","","from __future__ import annotations","import copy","from numbers import Number","import numpy as np","","from qiskit.exceptions import QiskitError","from qiskit.quantum_info.operators.base_operator import BaseOperator","from qiskit.quantum_info.operators.linear_op import LinearOp","from qiskit.quantum_info.operators.operator import Operator","from qiskit.quantum_info.operators.mixins import generate_apidocs","","","class ScalarOp(LinearOp):"," \"\"\"Scalar identity operator class.",""," This is a symbolic representation of an scalar identity operator on"," multiple subsystems. It may be used to initialize a symbolic scalar"," multiplication of an identity and then be implicitly converted to other"," kinds of operator subclasses by using the :meth:`compose`, :meth:`dot`,"," :meth:`tensor`, :meth:`expand` methods."," \"\"\"",""," def __init__(self, dims: int | tuple | None = None, coeff: Number = 1):"," \"\"\"Initialize an operator object.",""," Args:"," dims (int or tuple): subsystem dimensions."," coeff (Number): scalar coefficient for the identity"," operator (Default: 1).",""," Raises:"," QiskitError: If the optional coefficient is invalid."," \"\"\""," if not isinstance(coeff, Number):"," raise QiskitError(f\"coeff {coeff} must be a number.\")"," self._coeff = coeff"," super().__init__(input_dims=dims, output_dims=dims)",""," def __array__(self, dtype=None):"," if dtype:"," return np.asarray(self.to_matrix(), dtype=dtype)"," return self.to_matrix()",""," def __repr__(self):"," return f\"ScalarOp({self.input_dims()}, coeff={self.coeff})\"",""," @property"," def coeff(self):"," \"\"\"Return the coefficient\"\"\""," return self._coeff",""," def conjugate(self):"," ret = self.copy()"," ret._coeff = np.conjugate(self.coeff)"," return ret",""," def transpose(self):"," return self.copy()",""," def is_unitary(self, atol=None, rtol=None):"," \"\"\"Return True if operator is a unitary matrix.\"\"\""," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol"," return np.isclose(np.abs(self.coeff), 1, atol=atol, rtol=rtol)",""," def to_matrix(self):"," \"\"\"Convert to a Numpy matrix.\"\"\""," dim, _ = self.dim"," iden = np.eye(dim, dtype=complex)"," return self.coeff * iden",""," def to_operator(self) -> Operator:"," \"\"\"Convert to an Operator object.\"\"\""," return Operator("," self.to_matrix(), input_dims=self.input_dims(), output_dims=self.output_dims()"," )",""," def compose(self, other: ScalarOp, qargs: list | None = None, front: bool = False) -> ScalarOp:"," if qargs is None:"," qargs = getattr(other, \"qargs\", None)"," if not isinstance(other, BaseOperator):"," other = Operator(other)",""," new_shape = self._op_shape.compose(other._op_shape, qargs, front)",""," # If other is also an ScalarOp we only need to"," # update the coefficient and dimensions"," if isinstance(other, ScalarOp):"," ret = copy.copy(self)"," ret._coeff = self.coeff * other.coeff"," ret._op_shape = new_shape"," return ret",""," # If we are composing on the full system we return the"," # other operator with reshaped dimensions"," if qargs is None:"," ret = copy.copy(other)"," ret._op_shape = new_shape"," # Other operator might not support scalar multiplication"," # so we treat the identity as a special case to avoid a"," # possible error"," if self.coeff == 1:"," return ret"," return self.coeff * ret",""," # For qargs composition we initialize the scalar operator"," # as an instance of the other BaseOperators subclass. We then"," # perform subsystem qargs composition using the BaseOperator"," # subclasses compose method."," # Note that this will raise an error if the other operator does"," # not support initialization from a ScalarOp or the ScalarOps"," # `to_operator` method)."," return other.__class__(self).compose(other, qargs=qargs, front=front)",""," def power(self, n: float) -> ScalarOp:"," \"\"\"Return the power of the ScalarOp.",""," Args:"," n (float): the exponent for the scalar op.",""," Returns:"," ScalarOp: the ``coeff ** n`` ScalarOp."," \"\"\""," ret = self.copy()"," ret._coeff = self.coeff**n"," return ret",""," def tensor(self, other: ScalarOp) -> ScalarOp:"," if not isinstance(other, BaseOperator):"," other = Operator(other)",""," if isinstance(other, ScalarOp):"," ret = copy.copy(self)"," ret._coeff = self.coeff * other.coeff"," ret._op_shape = self._op_shape.tensor(other._op_shape)"," return ret",""," return other.expand(self)",""," def expand(self, other: ScalarOp) -> ScalarOp:"," if not isinstance(other, BaseOperator):"," other = Operator(other)",""," if isinstance(other, ScalarOp):"," ret = copy.copy(self)"," ret._coeff = self.coeff * other.coeff"," ret._op_shape = self._op_shape.expand(other._op_shape)"," return ret",""," return other.tensor(self)",""," def _add(self, other, qargs=None):"," \"\"\"Return the operator self + other.",""," If ``qargs`` are specified the other operator will be added"," assuming it is identity on all other subsystems.",""," Args:"," other (BaseOperator): an operator object."," qargs (None or list): optional subsystems to subtract on"," (Default: None)",""," Returns:"," ScalarOp: if other is an ScalarOp."," BaseOperator: if other is not an ScalarOp.",""," Raises:"," QiskitError: if other has incompatible dimensions."," \"\"\""," if qargs is None:"," qargs = getattr(other, \"qargs\", None)",""," if not isinstance(other, BaseOperator):"," other = Operator(other)",""," self._op_shape._validate_add(other._op_shape, qargs)",""," # Next if we are adding two ScalarOps we return a ScalarOp"," if isinstance(other, ScalarOp):"," return ScalarOp(self.input_dims(), coeff=self.coeff + other.coeff)",""," # If qargs are specified we have to pad the other BaseOperator"," # with identities on remaining subsystems. 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