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Add XXMinusYYGate (Qiskit#7799)
* add XXMinusYYGate * update docs and release note * move tests to existing files * update docs and release note Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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‎qiskit/circuit/library/standard_gates/__init__.py‎

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RZGate
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RZZGate
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RZXGate
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XXMinusYYGate
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XXPlusYYGate
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ECRGate
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SGate
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from .rz import RZGate, CRZGate
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from .rzz import RZZGate
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from .rzx import RZXGate
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from .xx_minus_yy import XXMinusYYGate
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from .xx_plus_yy import XXPlusYYGate
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from .ecr import ECRGate
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from .s import SGate, SdgGate

‎qiskit/circuit/library/standard_gates/xx_minus_yy.py‎

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# This code is part of Qiskit.
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#
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# (C) Copyright IBM 2021.
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#
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# This code is licensed under the Apache License, Version 2.0. You may
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# obtain a copy of this license in the LICENSE.txt file in the root directory
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# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
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#
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# Any modifications or derivative works of this code must retain this
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# copyright notice, and modified files need to carry a notice indicating
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# that they have been altered from the originals.
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"""Two-qubit XX-YY gate."""
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from typing import Optional
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import numpy as np
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from qiskit.circuit.gate import Gate
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from qiskit.circuit.library.standard_gates.ry import RYGate
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from qiskit.circuit.library.standard_gates.rz import RZGate
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from qiskit.circuit.library.standard_gates.s import SdgGate, SGate
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from qiskit.circuit.library.standard_gates.sx import SXdgGate, SXGate
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from qiskit.circuit.library.standard_gates.x import CXGate
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from qiskit.circuit.parameterexpression import ParameterValueType
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from qiskit.circuit.quantumcircuit import QuantumCircuit
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from qiskit.circuit.quantumregister import QuantumRegister
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from qiskit.qasm import pi
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class XXMinusYYGate(Gate):
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r"""XX-YY interaction gate.
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A 2-qubit parameterized XX-YY interaction. Its action is to induce
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a coherent rotation by some angle between :math:`|00\rangle` and :math:`|11\rangle`.
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**Circuit Symbol:**
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.. parsed-literal::
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┌───────────────┐
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q_0: ┤0 ├
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│ {XX-YY}(θ,β) │
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q_1: ┤1 ├
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└───────────────┘
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**Matrix Representation:**
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.. math::
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\newcommand{\th}{\frac{\theta}{2}}
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R_{XX-YY}(\theta, \beta) q_0, q_1 =
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RZ_1(\beta) \cdot exp(-i \frac{\theta}{2} \frac{XX-YY}{2}) \cdot RZ_1(-\beta) =
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\begin{pmatrix}
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\cos(\th) & 0 & 0 & -i\sin(\th)e^{-i\beta} \\
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0 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
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-i\sin(\th)e^{i\beta} & 0 & 0 & \cos(\th)
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\end{pmatrix}
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.. note::
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In Qiskit's convention, higher qubit indices are more significant
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(little endian convention). In the above example we apply the gate
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on (q_0, q_1) which results in adding the (optional) phase defined
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by :math:`beta` on q_1. Instead, if we apply it on (q_1, q_0), the
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phase is added on q_0. If :math:`beta` is set to its default value
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of :math:`0`, the gate is equivalent in big and little endian.
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.. parsed-literal::
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┌───────────────┐
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q_0: ┤1 ├
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│ {XX-YY}(θ,β) │
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q_1: ┤0 ├
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└───────────────┘
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.. math::
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\newcommand{\th}{\frac{\theta}{2}}
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R_{XX-YY}(\theta, \beta) q_1, q_0 =
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RZ_0(\beta) \cdot exp(-i \frac{\theta}{2} \frac{XX-YY}{2}) \cdot RZ_0(-\beta) =
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\begin{pmatrix}
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\cos(\th) & 0 & 0 & -i\sin(\th)e^{i\beta} \\
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0 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
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-i\sin(\th)e^{-i\beta} & 0 & 0 & \cos(\th)
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\end{pmatrix}
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"""
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def __init__(
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self,
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theta: ParameterValueType,
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beta: ParameterValueType = 0,
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label: Optional[str] = "{XX-YY}",
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):
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"""Create new XX-YY gate.
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Args:
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theta: The rotation angle.
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beta: The phase angle.
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label: The label of the gate.
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"""
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super().__init__("xx_minus_yy", 2, [theta, beta], label=label)
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def _define(self):
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"""
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gate xx_minus_yy(theta, beta) a, b {
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rz(-beta) b;
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rz(-pi/2) a;
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sx a;
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rz(pi/2) a;
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s b;
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cx a, b;
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ry(theta/2) a;
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ry(-theta/2) b;
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cx a, b;
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sdg b;
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rz(-pi/2) a;
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sxdg a;
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rz(pi/2) a;
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rz(beta) b;
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}
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"""
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theta, beta = self.params
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register = QuantumRegister(2, "q")
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circuit = QuantumCircuit(register, name=self.name)
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a, b = register
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rules = [
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(RZGate(-beta), [b], []),
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(RZGate(-pi / 2), [a], []),
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(SXGate(), [a], []),
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(RZGate(pi / 2), [a], []),
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(SGate(), [b], []),
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(CXGate(), [a, b], []),
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(RYGate(theta / 2), [a], []),
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(RYGate(-theta / 2), [b], []),
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(CXGate(), [a, b], []),
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(SdgGate(), [b], []),
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(RZGate(-pi / 2), [a], []),
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(SXdgGate(), [a], []),
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(RZGate(pi / 2), [a], []),
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(RZGate(beta), [b], []),
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]
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for instr, qargs, cargs in rules:
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circuit._append(instr, qargs, cargs)
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self.definition = circuit
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def inverse(self):
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"""Inverse gate."""
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theta, beta = self.params
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return XXMinusYYGate(-theta, beta)
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def __array__(self, dtype=None):
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"""Gate matrix."""
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theta, beta = self.params
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cos = np.cos(theta / 2)
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sin = np.sin(theta / 2)
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return np.array(
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[
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[cos, 0, 0, -1j * sin * np.exp(-1j * beta)],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[-1j * sin * np.exp(1j * beta), 0, 0, cos],
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],
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dtype=dtype,
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)

‎releasenotes/notes/add-xxminusyy-gate-63e6530c23500de9.yaml‎

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---
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features:
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- |
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Adds a gate for the XX-YY interaction, accessible via
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:class:`qiskit.circuit.library.XXMinusYYGate`. This gate can be used
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to implement the bSwap gate and its powers. It also arises
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in the simulation of superconducting fermionic models.

‎test/python/circuit/test_extensions_standard.py‎

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from inspect import signature
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import warnings
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import numpy as np
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from scipy.linalg import expm
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from ddt import data, ddt, unpack
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from qiskit import ClassicalRegister, QuantumCircuit, QuantumRegister, execute
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from qiskit.qasm import pi
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from qiskit.exceptions import QiskitError
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from qiskit.circuit.exceptions import CircuitError
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from qiskit.test import QiskitTestCase
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from qiskit.circuit import Gate, ControlledGate
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from qiskit.circuit.library import U1Gate, U2Gate, U3Gate, CU1Gate, CU3Gate
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from qiskit.circuit.library import (
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U1Gate,
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U2Gate,
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U3Gate,
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CU1Gate,
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CU3Gate,
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XXMinusYYGate,
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RZGate,
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XGate,
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YGate,
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)
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from qiskit import BasicAer
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from qiskit.quantum_info import Pauli
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from qiskit.quantum_info.operators.predicates import matrix_equal, is_unitary_matrix
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self.assertEqual(instruction_set.instructions[2].params, [])
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@ddt
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class TestStandard2Q(QiskitTestCase):
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"""Standard Extension Test. Gates with two Qubits"""
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self.assertEqual(instruction_set.qargs[1], [self.qr[1], self.qr2[1]])
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self.assertEqual(instruction_set.instructions[2].params, [])
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@unpack
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@data(
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(0, 0, np.eye(4)),
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(
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np.pi / 2,
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np.pi / 2,
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np.array(
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[
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[np.sqrt(2) / 2, 0, 0, -np.sqrt(2) / 2],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[np.sqrt(2) / 2, 0, 0, np.sqrt(2) / 2],
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]
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),
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),
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(
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np.pi,
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np.pi / 2,
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np.array([[0, 0, 0, -1], [0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0]]),
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),
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(
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2 * np.pi,
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np.pi / 2,
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np.array([[-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]]),
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),
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(
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np.pi / 2,
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np.pi,
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np.array(
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[
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[np.sqrt(2) / 2, 0, 0, 1j * np.sqrt(2) / 2],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[1j * np.sqrt(2) / 2, 0, 0, np.sqrt(2) / 2],
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]
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),
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),
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(4 * np.pi, 0, np.eye(4)),
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)
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def test_xx_minus_yy_matrix(self, theta: float, beta: float, expected: np.ndarray):
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"""Test XX-YY matrix."""
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gate = XXMinusYYGate(theta, beta)
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np.testing.assert_allclose(np.array(gate), expected, atol=1e-7)
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def test_xx_minus_yy_exponential_formula(self):
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"""Test XX-YY exponential formula."""
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theta, beta = np.random.uniform(-10, 10, size=2)
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theta = np.pi / 2
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beta = 0.0
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gate = XXMinusYYGate(theta, beta)
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x = np.array(XGate())
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y = np.array(YGate())
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xx = np.kron(x, x)
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yy = np.kron(y, y)
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rz1 = np.kron(np.array(RZGate(beta)), np.eye(2))
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np.testing.assert_allclose(
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np.array(gate),
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rz1 @ expm(-0.25j * theta * (xx - yy)) @ rz1.T.conj(),
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atol=1e-7,
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)
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class TestStandard3Q(QiskitTestCase):
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"""Standard Extension Test. Gates with three Qubits"""

‎test/python/circuit/test_gate_definitions.py‎

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SXdgGate,
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CSXGate,
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RVGate,
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XXMinusYYGate,
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)
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from qiskit.circuit.library.standard_gates.equivalence_library import (
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rv = RVGate(0, 0, 0)
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self.assertTrue(np.array_equal(rv.to_matrix(), np.array([[1, 0], [0, 1]])))
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def test_xx_minus_yy_definition(self):
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"""Test XX-YY gate decomposition."""
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theta, beta = np.random.uniform(-10, 10, size=2)
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gate = XXMinusYYGate(theta, beta)
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circuit = QuantumCircuit(2)
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circuit.append(gate, [0, 1])
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decomposed_circuit = circuit.decompose()
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self.assertTrue(len(decomposed_circuit) > len(circuit))
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self.assertTrue(Operator(circuit).equiv(Operator(decomposed_circuit), atol=1e-7))
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@ddt
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class TestStandardGates(QiskitTestCase):

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