# This code is part of Qiskit. # # (C) Copyright IBM 2017. # # 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-pulse single-qubit gate.""" from __future__ import annotations import math from cmath import exp from typing import Optional, Union import numpy from qiskit.circuit.controlledgate import ControlledGate from qiskit.circuit.gate import Gate from qiskit.circuit.parameterexpression import ParameterValueType, ParameterExpression from qiskit._accelerate.circuit import StandardGate class U3Gate(Gate): r"""Generic single-qubit rotation gate with 3 Euler angles. .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: U3(\theta, \phi, \lambda) = U(\theta, \phi, \lambda) .. code-block:: python circuit = QuantumCircuit(1) circuit.u(theta, phi, lambda) Circuit symbol: .. code-block:: text ┌───────────┐ q_0: ┤ U3(ϴ,φ,λ) ├ └───────────┘ Matrix representation: .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} U3(\theta, \phi, \lambda) = \begin{pmatrix} \cos\left(\rotationangle\right) & -e^{i\lambda}\sin\left(\rotationangle\right) \\ e^{i\phi}\sin\left(\rotationangle\right) & e^{i(\phi+\lambda)}\cos\left(\rotationangle\right) \end{pmatrix} .. note:: The matrix representation shown here differs from the `OpenQASM 2.0 specification `_ by a global phase of :math:`e^{i(\phi+\lambda)/2}`. Examples: .. math:: U3(\theta, \phi, \lambda) = P(\phi) R_Y(\theta) P(\lambda) = e^{i\frac{\phi + \lambda}{2}} R_Z(\phi) R_Y(\theta) R_Z(\lambda) .. math:: U3\left(\theta, -\frac{\pi}{2}, \frac{\pi}{2}\right) = RX(\theta) .. math:: U3(\theta, 0, 0) = RY(\theta) """ _standard_gate = StandardGate.U3 def __init__( self, theta: ParameterValueType, phi: ParameterValueType, lam: ParameterValueType, label: Optional[str] = None, ): r""" Args: theta: The angle :math:`\theta corresponding to the :math:`R_Y(\theta)` rotation. phi: The angle :math:`\phi` corresponding to the :math:`R_Z(\phi)` rotation. lam: The angle :math:`\lambda` corresponding to the :math:`R_Z(\lambda)` rotation. label: An optional label for the gate. """ super().__init__("u3", 1, [theta, phi, lam], label=label) def inverse(self, annotated: bool = False): r"""Return inverted U3 gate. :math:`U3(\theta,\phi,\lambda)^{\dagger} =U3(-\theta,-\lambda,-\phi))` 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:`.U3Gate` with inverse parameter values. Returns: U3Gate: inverse gate. """ return U3Gate(-self.params[0], -self.params[2], -self.params[1]) 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-U3 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 and more than one control qubit, in which case it cannot yet be synthesized. Otherwise it is set to ``False``. Returns: ControlledGate: controlled version of this gate. """ if not annotated and num_ctrl_qubits == 1: gate = CU3Gate(*self.params, label=label, ctrl_state=ctrl_state) gate.base_gate.label = self.label else: # If the gate parameters contain free parameters, we cannot eagerly synthesize # the controlled gate decomposition. In this case, we annotate the gate per default. 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 _define(self): """Default definition""" # pylint: disable=cyclic-import from qiskit.circuit import QuantumCircuit # ┌──────────┐ # q: ┤ U(θ,φ,λ) ├ # └──────────┘ self.definition = QuantumCircuit._from_circuit_data( StandardGate.U3._get_definition(self.params), legacy_qubits=True, name=self.name ) def __array__(self, dtype=None, copy=None): """Return a Numpy.array for the U3 gate.""" if copy is False: raise ValueError("unable to avoid copy while creating an array as requested") theta, phi, lam = self.params theta, phi, lam = float(theta), float(phi), float(lam) cos = math.cos(theta / 2) sin = math.sin(theta / 2) return numpy.array( [ [cos, -exp(1j * lam) * sin], [exp(1j * phi) * sin, exp(1j * (phi + lam)) * cos], ], dtype=dtype or complex, ) def __eq__(self, other): return isinstance(other, U3Gate) and self._compare_parameters(other) class CU3Gate(ControlledGate): r"""Controlled-U3 gate (3-parameter two-qubit gate). This is a controlled version of the U3 gate (generic single qubit rotation). It is restricted to 3 parameters, and so cannot cover generic two-qubit controlled gates). .. warning:: This gate is deprecated. Instead, the :class:`.CUGate` should be used .. math:: CU3(\theta, \phi, \lambda) = CU(\theta, \phi, \lambda, 0) .. code-block:: python circuit = QuantumCircuit(2) gamma = 0 circuit.cu(theta, phi, lambda, gamma, 0, 1) Circuit symbol: .. code-block:: text q_0: ──────■────── ┌─────┴─────┐ q_1: ┤ U3(ϴ,φ,λ) ├ └───────────┘ Matrix representation: .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} CU3(\theta, \phi, \lambda)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + U3(\theta,\phi,\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\rotationangle) & 0 & -e^{i\lambda}\sin(\rotationangle) \\ 0 & 0 & 1 & 0 \\ 0 & e^{i\phi}\sin(\rotationangle) & 0 & e^{i(\phi+\lambda)}\cos(\rotationangle) \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be: .. code-block:: text ┌───────────┐ q_0: ┤ U3(ϴ,φ,λ) ├ └─────┬─────┘ q_1: ──────■────── .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} CU3(\theta, \phi, \lambda)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes U3(\theta,\phi,\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\rotationangle) & -e^{i\lambda}\sin(\rotationangle) \\ 0 & 0 & e^{i\phi}\sin(\rotationangle) & e^{i(\phi+\lambda)}\cos(\rotationangle) \end{pmatrix} """ _standard_gate = StandardGate.CU3 def __init__( self, theta: ParameterValueType, phi: ParameterValueType, lam: ParameterValueType, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None, *, _base_label=None, ): """Create new CU3 gate.""" super().__init__( "cu3", 2, [theta, phi, lam], num_ctrl_qubits=1, label=label, ctrl_state=ctrl_state, base_gate=U3Gate(theta, phi, lam, label=_base_label), ) def _define(self): """Default definition""" # pylint: disable=cyclic-import from qiskit.circuit import QuantumCircuit # ┌──────────────┐ # q_0: ┤ P(λ/2 + φ/2) ├──■────────────────────────────■──────────────── # ├──────────────┤┌─┴─┐┌──────────────────────┐┌─┴─┐┌────────────┐ # q_1: ┤ P(λ/2 - φ/2) ├┤ X ├┤ U(-θ/2,0,-λ/2 - φ/2) ├┤ X ├┤ U(θ/2,φ,0) ├ # └──────────────┘└───┘└──────────────────────┘└───┘└────────────┘ self.definition = QuantumCircuit._from_circuit_data( StandardGate.CU3._get_definition(self.params), legacy_qubits=True, name=self.name ) def inverse(self, annotated: bool = False): r"""Return inverted CU3 gate. :math:`CU3(\theta,\phi,\lambda)^{\dagger} =CU3(-\theta,-\phi,-\lambda))` 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:`.CU3Gate` with inverse parameter values. Returns: CU3Gate: inverse gate. """ return CU3Gate( -self.params[0], -self.params[2], -self.params[1], ctrl_state=self.ctrl_state ) def __array__(self, dtype=None, copy=None): """Return a numpy.array for the CU3 gate.""" if copy is False: raise ValueError("unable to avoid copy while creating an array as requested") theta, phi, lam = self.params theta, phi, lam = float(theta), float(phi), float(lam) cos = math.cos(theta / 2) sin = math.sin(theta / 2) if self.ctrl_state: return numpy.array( [ [1, 0, 0, 0], [0, cos, 0, -exp(1j * lam) * sin], [0, 0, 1, 0], [0, exp(1j * phi) * sin, 0, exp(1j * (phi + lam)) * cos], ], dtype=dtype or complex, ) else: return numpy.array( [ [cos, 0, -exp(1j * lam) * sin, 0], [0, 1, 0, 0], [exp(1j * phi) * sin, 0, exp(1j * (phi + lam)) * cos, 0], [0, 0, 0, 1], ], dtype=dtype or complex, ) def __eq__(self, other): return ( isinstance(other, CU3Gate) and self.ctrl_state == other.ctrl_state and self._compare_parameters(other) ) def _generate_gray_code(num_bits): """Generate the gray code for ``num_bits`` bits.""" if num_bits <= 0: raise ValueError("Cannot generate the gray code for less than 1 bit.") result = [0] for i in range(num_bits): result += [x + 2**i for x in reversed(result)] return [format(x, f"0{num_bits}b") for x in result] def _gray_code_chain(q, num_ctrl_qubits, gate): """Apply the gate to the last qubit in the register ``q``, controlled on all preceding qubits. This function uses the gray code to propagate down to the last qubit. Ported and adapted from Aqua (github.com/Qiskit/qiskit-aqua), commit 769ca8d, file qiskit/aqua/circuits/gates/multi_control_u1_gate.py. """ from .x import CXGate rule = [] q_controls, q_target = q[:num_ctrl_qubits], q[num_ctrl_qubits] gray_code = _generate_gray_code(num_ctrl_qubits) last_pattern = None for pattern in gray_code: if "1" not in pattern: continue if last_pattern is None: last_pattern = pattern # find left most set bit lm_pos = list(pattern).index("1") # find changed bit comp = [i != j for i, j in zip(pattern, last_pattern)] if True in comp: pos = comp.index(True) else: pos = None if pos is not None: if pos != lm_pos: rule.append((CXGate(), [q_controls[pos], q_controls[lm_pos]], [])) else: indices = [i for i, x in enumerate(pattern) if x == "1"] for idx in indices[1:]: rule.append((CXGate(), [q_controls[idx], q_controls[lm_pos]], [])) # check parity if pattern.count("1") % 2 == 0: # inverse rule.append((gate.inverse(), [q_controls[lm_pos], q_target], [])) else: rule.append((gate, [q_controls[lm_pos], q_target], [])) last_pattern = pattern return rule