# 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 from typing import TYPE_CHECKING import numpy as np from qiskit._accelerate import euler_one_qubit_decomposer from qiskit.circuit.quantumcircuit import QuantumCircuit from qiskit.circuit 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 if TYPE_CHECKING: from qiskit.dagcircuit import DAGCircuit 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, } 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 (:math:`U3`, :math:`U1X`, :math:`RR`), the :math:`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)` .. automethod:: __call__ """ 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: the decomposition basis [Default: ``'U3'``] use_dag: 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 def build_circuit(self, gates, global_phase) -> QuantumCircuit | DAGCircuit: """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 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].name](*gate_entry[1]) else: gate = gate_entry.name dag.apply_operation_back(gate, (qr[0],), check=False) return dag def __call__( self, unitary: Operator | Gate | np.ndarray, simplify: bool = True, atol: float = DEFAULT_ATOL, ) -> QuantumCircuit | DAGCircuit: """Decompose single qubit gate into a circuit. Args: unitary: 1-qubit unitary matrix simplify: reduce gate count in decomposition [Default: True]. atol: 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): if self.use_dag: 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 return QuantumCircuit._from_circuit_data( euler_one_qubit_decomposer.unitary_to_circuit( unitary, [self.basis], 0, None, simplify, atol ), legacy_qubits=True, ) @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] def angles(self, unitary: np.ndarray) -> tuple: """Return the Euler angles for input array. Args: unitary: :math:`2\\times2` unitary matrix. Returns: tuple: ``(theta, phi, lambda)``. """ unitary = np.asarray(unitary, dtype=complex) theta, phi, lam, _ = self._params(unitary) return theta, phi, lam def angles_and_phase(self, unitary: np.ndarray) -> tuple: """Return the Euler angles and phase for input array. Args: unitary: :math:`2\\times2` 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)