# 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.
"""
Decompose a single-qubit unitary via Euler angles.
"""
from __future__ import annotations
import numpy as np
from qiskit._accelerate import euler_one_qubit_decomposer
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.quantumregister import Qubit
from qiskit.circuit.library.standard_gates import (
UGate,
PhaseGate,
U3Gate,
U2Gate,
U1Gate,
RXGate,
RYGate,
RZGate,
RGate,
SXGate,
XGate,
)
from qiskit.exceptions import QiskitError
from qiskit.quantum_info.operators.predicates import is_unitary_matrix
from qiskit.circuit.gate import Gate
from qiskit.quantum_info.operators.operator import Operator
DEFAULT_ATOL = 1e-12
ONE_QUBIT_EULER_BASIS_GATES = {
"U3": ["u3"],
"U321": ["u3", "u2", "u1"],
"U": ["u"],
"PSX": ["p", "sx"],
"U1X": ["u1", "rx"],
"RR": ["r"],
"ZYZ": ["rz", "ry"],
"ZXZ": ["rz", "rx"],
"XZX": ["rz", "rx"],
"XYX": ["rx", "ry"],
"ZSXX": ["rz", "sx", "x"],
"ZSX": ["rz", "sx"],
}
NAME_MAP = {
"u": UGate,
"u1": U1Gate,
"u2": U2Gate,
"u3": U3Gate,
"p": PhaseGate,
"rx": RXGate,
"ry": RYGate,
"rz": RZGate,
"r": RGate,
"sx": SXGate,
"x": XGate,
}
[docs]class OneQubitEulerDecomposer:
r"""A class for decomposing 1-qubit unitaries into Euler angle rotations.
The resulting decomposition is parameterized by 3 Euler rotation angle
parameters :math:`(\theta, \phi, \lambda)`, and a phase parameter
:math:`\gamma`. The value of the parameters for an input unitary depends
on the decomposition basis. Allowed bases and the resulting circuits are
shown in the following table. Note that for the non-Euler bases (U3, U1X,
RR), the ZYZ Euler parameters are used.
.. list-table:: Supported circuit bases
:widths: auto
:header-rows: 1
* - Basis
- Euler Angle Basis
- Decomposition Circuit
* - 'ZYZ'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} R_Z(\phi).R_Y(\theta).R_Z(\lambda)`
* - 'ZXZ'
- :math:`Z(\phi) X(\theta) Z(\lambda)`
- :math:`e^{i\gamma} R_Z(\phi).R_X(\theta).R_Z(\lambda)`
* - 'XYX'
- :math:`X(\phi) Y(\theta) X(\lambda)`
- :math:`e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)`
* - 'XZX'
- :math:`X(\phi) Z(\theta) X(\lambda)`
- :math:`e^{i\gamma} R_X(\phi).R_Z(\theta).R_X(\lambda)`
* - 'U3'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} U_3(\theta,\phi,\lambda)`
* - 'U321'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} U_3(\theta,\phi,\lambda)`
* - 'U'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} U_3(\theta,\phi,\lambda)`
* - 'PSX'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).`
:math:`U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)`
* - 'ZSX'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.`
:math:`R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)`
* - 'ZSXX'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)`
or
:math:`e^{i\gamma} R_Z(\phi+\pi).X.R_Z(\lambda)`
* - 'U1X'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).`
:math:`U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)`
* - 'RR'
- :math:`Z(\phi) Y(\theta) Z(\lambda)`
- :math:`e^{i\gamma} R\left(-\pi,\frac{\phi-\lambda+\pi}{2}\right).`
:math:`R\left(\theta+\pi,\frac{\pi}{2}-\lambda\right)`
"""
def __init__(self, basis: str = "U3", use_dag: bool = False):
"""Initialize decomposer
Supported bases are: 'U', 'PSX', 'ZSXX', 'ZSX', 'U321', 'U3', 'U1X', 'RR', 'ZYZ', 'ZXZ',
'XYX', 'XZX'.
Args:
basis (str): the decomposition basis [Default: 'U3']
use_dag (bool): If true the output from calls to the decomposer
will be a :class:`~qiskit.dagcircuit.DAGCircuit` object instead of
:class:`~qiskit.circuit.QuantumCircuit`.
Raises:
QiskitError: If input basis is not recognized.
"""
self.basis = basis # sets: self._basis, self._params, self._circuit
self.use_dag = use_dag
[docs] def build_circuit(self, gates, global_phase):
"""Return the circuit or dag object from a list of gates."""
qr = [Qubit()]
lookup_gate = False
if len(gates) > 0 and isinstance(gates[0], tuple):
lookup_gate = True
if self.use_dag:
from qiskit.dagcircuit import dagcircuit
dag = dagcircuit.DAGCircuit()
dag.global_phase = global_phase
dag.add_qubits(qr)
for gate_entry in gates:
if lookup_gate:
gate = NAME_MAP[gate_entry[0]](*gate_entry[1])
else:
gate = gate_entry
dag.apply_operation_back(gate, [qr[0]])
return dag
else:
circuit = QuantumCircuit(qr, global_phase=global_phase)
for gate_entry in gates:
if lookup_gate:
gate = NAME_MAP[gate_entry[0]](*gate_entry[1])
else:
gate = gate_entry
circuit._append(gate, [qr[0]], [])
return circuit
def __call__(
self,
unitary: Operator | Gate | np.ndarray,
simplify: bool = True,
atol: float = DEFAULT_ATOL,
) -> QuantumCircuit:
"""Decompose single qubit gate into a circuit.
Args:
unitary (Operator or Gate or array): 1-qubit unitary matrix
simplify (bool): reduce gate count in decomposition [Default: True].
atol (float): absolute tolerance for checking angles when simplifying
returned circuit [Default: 1e-12].
Returns:
QuantumCircuit: the decomposed single-qubit gate circuit
Raises:
QiskitError: if input is invalid or synthesis fails.
"""
if hasattr(unitary, "to_operator"):
# If input is a BaseOperator subclass this attempts to convert
# the object to an Operator so that we can extract the underlying
# numpy matrix from `Operator.data`.
unitary = unitary.to_operator().data
elif hasattr(unitary, "to_matrix"):
# If input is Gate subclass or some other class object that has
# a to_matrix method this will call that method.
unitary = unitary.to_matrix()
# Convert to numpy array in case not already an array
unitary = np.asarray(unitary, dtype=complex)
# Check input is a 2-qubit unitary
if unitary.shape != (2, 2):
raise QiskitError("OneQubitEulerDecomposer: expected 2x2 input matrix")
if not is_unitary_matrix(unitary):
raise QiskitError("OneQubitEulerDecomposer: input matrix is not unitary.")
return self._decompose(unitary, simplify=simplify, atol=atol)
def _decompose(self, unitary, simplify=True, atol=DEFAULT_ATOL):
circuit_sequence = euler_one_qubit_decomposer.unitary_to_gate_sequence(
unitary, [self.basis], 0, None, simplify, atol
)
circuit = self.build_circuit(circuit_sequence, circuit_sequence.global_phase)
return circuit
@property
def basis(self):
"""The decomposition basis."""
return self._basis
@basis.setter
def basis(self, basis):
"""Set the decomposition basis."""
basis_methods = {
"U321": self._params_u3,
"U3": self._params_u3,
"U": self._params_u3,
"PSX": self._params_u1x,
"ZSX": self._params_u1x,
"ZSXX": self._params_u1x,
"U1X": self._params_u1x,
"RR": self._params_zyz,
"ZYZ": self._params_zyz,
"ZXZ": self._params_zxz,
"XYX": self._params_xyx,
"XZX": self._params_xzx,
}
if basis not in basis_methods:
raise QiskitError(f"OneQubitEulerDecomposer: unsupported basis {basis}")
self._basis = basis
self._params = basis_methods[basis]
[docs] def angles(self, unitary: np.ndarray) -> tuple:
"""Return the Euler angles for input array.
Args:
unitary (np.ndarray): 2x2 unitary matrix.
Returns:
tuple: (theta, phi, lambda).
"""
unitary = np.asarray(unitary, dtype=complex)
theta, phi, lam, _ = self._params(unitary)
return theta, phi, lam
[docs] def angles_and_phase(self, unitary: np.ndarray) -> tuple:
"""Return the Euler angles and phase for input array.
Args:
unitary (np.ndarray): 2x2 unitary matrix.
Returns:
tuple: (theta, phi, lambda, phase).
"""
unitary = np.asarray(unitary, dtype=complex)
return self._params(unitary)
_params_zyz = staticmethod(euler_one_qubit_decomposer.params_zyz)
_params_zxz = staticmethod(euler_one_qubit_decomposer.params_zxz)
_params_xyx = staticmethod(euler_one_qubit_decomposer.params_xyx)
_params_xzx = staticmethod(euler_one_qubit_decomposer.params_xzx)
_params_u3 = staticmethod(euler_one_qubit_decomposer.params_u3)
_params_u1x = staticmethod(euler_one_qubit_decomposer.params_u1x)