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cnotdihedral_decompose_two_qubits.py
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cnotdihedral_decompose_two_qubits.py
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# This code is part of Qiskit.
#
# (C) Copyright IBM 2019, 2024.
#
# 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.
"""
Circuit synthesis for the CNOTDihedral class.
"""
import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.exceptions import QiskitError
from qiskit.quantum_info import CNOTDihedral
def synth_cnotdihedral_two_qubits(elem: CNOTDihedral) -> QuantumCircuit:
"""Decompose a :class:`.CNOTDihedral` element on a single qubit and two
qubits into a :class:`.QuantumCircuit`.
This decomposition has an optimal number of :class:`.CXGate`\\ s.
Args:
elem: A :class:`.CNOTDihedral` element.
Returns:
A circuit implementation of the :class:`.CNOTDihedral` element.
Raises:
QiskitError: if the element in not 1-qubit or 2-qubit :class:`.CNOTDihedral`.
References:
1. Shelly Garion and Andrew W. Cross, *On the structure of the CNOT-Dihedral group*,
`arXiv:2006.12042 [quant-ph] <https://arxiv.org/abs/2006.12042>`_
"""
circuit = QuantumCircuit(elem.num_qubits)
if elem.num_qubits > 2:
raise QiskitError(
"Cannot decompose a CNOT-Dihedral element with more than 2 qubits. "
"use synth_cnotdihedral_full function instead."
)
if elem.num_qubits == 1:
if elem.poly.weight_0 != 0 or elem.linear != [[1]]:
raise QiskitError("1-qubit element in not CNOT-Dihedral .")
tpow0 = elem.poly.weight_1[0]
xpow0 = elem.shift[0]
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow0 == 0 and xpow0 == 0:
circuit.id(0)
return circuit
# case elem.num_qubits == 2:
if elem.poly.weight_0 != 0:
raise QiskitError("2-qubit element in not CNOT-Dihedral .")
weight_1 = elem.poly.weight_1
weight_2 = elem.poly.weight_2
linear = elem.linear
shift = elem.shift
# CS subgroup
if (linear == [[1, 0], [0, 1]]).all():
[xpow0, xpow1] = shift
# Dihedral class
if weight_2 == [0]:
[tpow0, tpow1] = weight_1
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
if tpow0 == 0 and tpow1 == 0 and xpow0 == 0 and xpow1 == 0:
circuit.id(0)
circuit.id(1)
# CS-like class
if (weight_2 == [2] and xpow0 == xpow1) or (weight_2 == [6] and xpow0 != xpow1):
tpow0 = (weight_1[0] - 2 * xpow1 - 4 * xpow0 * xpow1) % 8
tpow1 = (weight_1[1] - 2 * xpow0 - 4 * xpow0 * xpow1) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
# CS gate is implemented using 2 CX gates
circuit.p((np.pi / 4), [0])
circuit.p((np.pi / 4), [1])
circuit.cx(0, 1)
circuit.p((7 * np.pi / 4), [1])
circuit.cx(0, 1)
# CSdg-like class
if (weight_2 == [6] and xpow0 == xpow1) or (weight_2 == [2] and xpow0 != xpow1):
tpow0 = (weight_1[0] - 6 * xpow1 - 4 * xpow0 * xpow1) % 8
tpow1 = (weight_1[1] - 6 * xpow0 - 4 * xpow0 * xpow1) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
# CSdg gate is implemented using 2 CX gates
circuit.p((7 * np.pi / 4), [0])
circuit.p((7 * np.pi / 4), [1])
circuit.cx(0, 1)
circuit.p((np.pi / 4), [1])
circuit.cx(0, 1)
# CZ-like class
if weight_2 == [4]:
tpow0 = (weight_1[0] - 4 * xpow1) % 8
tpow1 = (weight_1[1] - 4 * xpow0) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
# CZ gate is implemented using 2 CX gates
circuit.cz(1, 0)
# CX01-like class
if (linear == [[1, 0], [1, 1]]).all():
xpow0 = shift[0]
xpow1 = (shift[1] + xpow0) % 2
if xpow0 == xpow1:
m = ((8 - weight_2[0]) / 2) % 4
tpow0 = (weight_1[0] - m) % 8
tpow1 = (weight_1[1] - m) % 8
else:
m = (weight_2[0] / 2) % 4
tpow0 = (weight_1[0] + m) % 8
tpow1 = (weight_1[1] + m) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
circuit.cx(0, 1)
if m > 0:
circuit.p((m * np.pi / 4), [1])
# CX10-like class
if (linear == [[1, 1], [0, 1]]).all():
xpow1 = shift[1]
xpow0 = (shift[0] + xpow1) % 2
if xpow0 == xpow1:
m = ((8 - weight_2[0]) / 2) % 4
tpow0 = (weight_1[0] - m) % 8
tpow1 = (weight_1[1] - m) % 8
else:
m = (weight_2[0] / 2) % 4
tpow0 = (weight_1[0] + m) % 8
tpow1 = (weight_1[1] + m) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
circuit.cx(1, 0)
if m > 0:
circuit.p((m * np.pi / 4), [0])
# CX01*CX10-like class
if (linear == [[0, 1], [1, 1]]).all():
xpow1 = shift[0]
xpow0 = (shift[1] + xpow1) % 2
if xpow0 == xpow1:
m = ((8 - weight_2[0]) / 2) % 4
tpow0 = (weight_1[0] - m) % 8
tpow1 = (weight_1[1] - m) % 8
else:
m = (weight_2[0] / 2) % 4
tpow0 = (weight_1[0] + m) % 8
tpow1 = (weight_1[1] + m) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
circuit.cx(0, 1)
circuit.cx(1, 0)
if m > 0:
circuit.p((m * np.pi / 4), [1])
# CX10*CX01-like class
if (linear == [[1, 1], [1, 0]]).all():
xpow0 = shift[1]
xpow1 = (shift[0] + xpow0) % 2
if xpow0 == xpow1:
m = ((8 - weight_2[0]) / 2) % 4
tpow0 = (weight_1[0] - m) % 8
tpow1 = (weight_1[1] - m) % 8
else:
m = (weight_2[0] / 2) % 4
tpow0 = (weight_1[0] + m) % 8
tpow1 = (weight_1[1] + m) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
circuit.cx(1, 0)
circuit.cx(0, 1)
if m > 0:
circuit.p((m * np.pi / 4), [0])
# CX01*CX10*CX01-like class
if (linear == [[0, 1], [1, 0]]).all():
xpow0 = shift[1]
xpow1 = shift[0]
if xpow0 == xpow1:
m = ((8 - weight_2[0]) / 2) % 4
tpow0 = (weight_1[0] - m) % 8
tpow1 = (weight_1[1] - m) % 8
else:
m = (weight_2[0] / 2) % 4
tpow0 = (weight_1[0] + m) % 8
tpow1 = (weight_1[1] + m) % 8
if tpow0 > 0:
circuit.p((tpow0 * np.pi / 4), [0])
if xpow0 == 1:
circuit.x(0)
if tpow1 > 0:
circuit.p((tpow1 * np.pi / 4), [1])
if xpow1 == 1:
circuit.x(1)
circuit.cx(0, 1)
circuit.cx(1, 0)
if m > 0:
circuit.p((m * np.pi / 4), [1])
circuit.cx(0, 1)
return circuit