# This code is part of Qiskit. # # (C) Copyright IBM 2021. # # 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. """Two-qubit XX-YY gate.""" from __future__ import annotations import math from cmath import exp from math import pi from typing import Optional import numpy as np from qiskit.circuit.gate import Gate from qiskit.circuit.library.standard_gates.ry import RYGate from qiskit.circuit.library.standard_gates.rz import RZGate from qiskit.circuit.library.standard_gates.s import SdgGate, SGate from qiskit.circuit.library.standard_gates.sx import SXdgGate, SXGate from qiskit.circuit.library.standard_gates.x import CXGate from qiskit.circuit.parameterexpression import ParameterValueType, ParameterExpression from qiskit.circuit.quantumcircuit import QuantumCircuit from qiskit.circuit.quantumregister import QuantumRegister from qiskit._accelerate.circuit import StandardGate class XXMinusYYGate(Gate): r"""XX-YY interaction gate. A 2-qubit parameterized XX-YY interaction. Its action is to induce a coherent rotation by some angle between :math:`|00\rangle` and :math:`|11\rangle`. **Circuit Symbol:** .. code-block:: text ┌───────────────┐ q_0: ┤0 ├ │ (XX-YY)(θ,β) │ q_1: ┤1 ├ └───────────────┘ **Matrix Representation:** .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} R_{XX-YY}(\theta, \beta) q_0, q_1 = RZ_1(\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX-YY}{2}\right) \cdot RZ_1(-\beta) = \begin{pmatrix} \cos\left(\rotationangle\right) & 0 & 0 & -i\sin\left(\rotationangle\right)e^{-i\beta} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -i\sin\left(\rotationangle\right)e^{i\beta} & 0 & 0 & \cos\left(\rotationangle\right) \end{pmatrix} """ _standard_gate = StandardGate.XXMinusYYGate def __init__( self, theta: ParameterValueType, beta: ParameterValueType = 0, label: Optional[str] = "(XX-YY)", *, duration=None, unit="dt", ): """Create new XX-YY gate. Args: theta: The rotation angle. beta: The phase angle. label: The label of the gate. """ super().__init__("xx_minus_yy", 2, [theta, beta], label=label, duration=duration, unit=unit) def _define(self): """ gate xx_minus_yy(theta, beta) a, b { rz(-beta) b; rz(-pi/2) a; sx a; rz(pi/2) a; s b; cx a, b; ry(theta/2) a; ry(-theta/2) b; cx a, b; sdg b; rz(-pi/2) a; sxdg a; rz(pi/2) a; rz(beta) b; } """ theta, beta = self.params register = QuantumRegister(2, "q") circuit = QuantumCircuit(register, name=self.name) a, b = register rules = [ (RZGate(-beta), [b], []), (RZGate(-pi / 2), [a], []), (SXGate(), [a], []), (RZGate(pi / 2), [a], []), (SGate(), [b], []), (CXGate(), [a, b], []), (RYGate(theta / 2), [a], []), (RYGate(-theta / 2), [b], []), (CXGate(), [a, b], []), (SdgGate(), [b], []), (RZGate(-pi / 2), [a], []), (SXdgGate(), [a], []), (RZGate(pi / 2), [a], []), (RZGate(beta), [b], []), ] for instr, qargs, cargs in rules: circuit._append(instr, qargs, cargs) self.definition = circuit def control( self, num_ctrl_qubits: int = 1, label: str | None = None, ctrl_state: str | int | None = None, annotated: bool | None = None, ): """Return a (multi-)controlled-(XX-YY) gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. If ``None``, this is set to ``True`` if the gate contains free parameters, in which case it cannot yet be synthesized. Returns: ControlledGate: controlled version of this gate. """ if annotated is None: annotated = any(isinstance(p, ParameterExpression) for p in self.params) gate = super().control( num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state, annotated=annotated, ) return gate def inverse(self, annotated: bool = False): """Inverse gate. Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.XXMinusYYGate` with inverse parameter values. Returns: XXMinusYYGate: inverse gate. """ theta, beta = self.params return XXMinusYYGate(-theta, beta) def __array__(self, dtype=None, copy=None): """Gate matrix.""" if copy is False: raise ValueError("unable to avoid copy while creating an array as requested") theta, beta = self.params cos = math.cos(theta / 2) sin = math.sin(theta / 2) return np.array( [ [cos, 0, 0, -1j * sin * exp(-1j * beta)], [0, 1, 0, 0], [0, 0, 1, 0], [-1j * sin * exp(1j * beta), 0, 0, cos], ], dtype=dtype, ) def power(self, exponent: float, annotated: bool = False): theta, beta = self.params return XXMinusYYGate(exponent * theta, beta) def __eq__(self, other): if isinstance(other, XXMinusYYGate): return self._compare_parameters(other) return False