# 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. """U1 Gate.""" from __future__ import annotations from cmath import exp import numpy from qiskit.circuit.controlledgate import ControlledGate from qiskit.circuit.gate import Gate from qiskit.circuit.parameterexpression import ParameterValueType from qiskit.circuit.quantumregister import QuantumRegister from qiskit.circuit._utils import _ctrl_state_to_int from qiskit._accelerate.circuit import StandardGate class U1Gate(Gate): r"""Single-qubit rotation about the Z axis. This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration). .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: U1(\theta) = P(\theta)= U(0,0,\theta) .. code-block:: python circuit = QuantumCircuit(1) circuit.p(lambda, 0) # or circuit.u(0, 0, lambda, 0) **Circuit symbol:** .. code-block:: text ┌───────┐ q_0: ┤ U1(θ) ├ └───────┘ **Matrix Representation:** .. math:: U1(\theta) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{pmatrix} **Examples:** .. math:: U1(\theta = \pi) = Z .. math:: U1(\theta = \pi/2) = S .. math:: U1(\theta = \pi/4) = T .. seealso:: :class:`~qiskit.circuit.library.standard_gates.RZGate`: This gate is equivalent to RZ up to a phase factor. .. math:: U1(\theta) = e^{i{\theta}/2} RZ(\theta) :class:`~qiskit.circuit.library.standard_gates.U3Gate`: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses. Reference for virtual Z gate implementation: `1612.00858 `_ """ _standard_gate = StandardGate.U1Gate def __init__( self, theta: ParameterValueType, label: str | None = None, *, duration=None, unit="dt" ): """Create new U1 gate.""" super().__init__("u1", 1, [theta], label=label, duration=duration, unit=unit) def _define(self): # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .u3 import U3Gate # pylint: disable=cyclic-import q = QuantumRegister(1, "q") qc = QuantumCircuit(q, name=self.name) rules = [(U3Gate(0, 0, self.params[0]), [q[0]], [])] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc def control( self, num_ctrl_qubits: int = 1, label: str | None = None, ctrl_state: str | int | None = None, annotated: bool = False, ): """Return a (multi-)controlled-U1 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. Returns: ControlledGate: controlled version of this gate. """ if not annotated and num_ctrl_qubits == 1: gate = CU1Gate(self.params[0], label=label, ctrl_state=ctrl_state) gate.base_gate.label = self.label elif not annotated and ctrl_state is None and num_ctrl_qubits > 1: gate = MCU1Gate(self.params[0], num_ctrl_qubits, label=label) gate.base_gate.label = self.label else: gate = super().control( num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state, annotated=annotated, ) return gate def inverse(self, annotated: bool = False): r"""Return inverted U1 gate (:math:`U1(\lambda)^{\dagger} = U1(-\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:`.U1Gate` with inverse parameter values. Returns: U1Gate: inverse gate. """ return U1Gate(-self.params[0]) def __array__(self, dtype=None, copy=None): """Return a numpy.array for the U1 gate.""" if copy is False: raise ValueError("unable to avoid copy while creating an array as requested") lam = float(self.params[0]) return numpy.array([[1, 0], [0, numpy.exp(1j * lam)]], dtype=dtype) def __eq__(self, other): return isinstance(other, U1Gate) and self._compare_parameters(other) class CU1Gate(ControlledGate): r"""Controlled-U1 gate. This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the control state. .. warning:: This gate is deprecated. Instead, the :class:`.CPhaseGate` should be used .. math:: CU1(\lambda) = CP(\lambda) .. code-block:: python circuit = QuantumCircuit(2) circuit.cp(lambda, 0, 1) **Circuit symbol:** .. code-block:: text q_0: ─■── │θ q_1: ─■── **Matrix representation:** .. math:: CU1(\theta) = I \otimes |0\rangle\langle 0| + U1 \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CRZGate`: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference. """ _standard_gate = StandardGate.CU1Gate def __init__( self, theta: ParameterValueType, label: str | None = None, ctrl_state: str | int | None = None, *, duration=None, unit="dt", _base_label=None, ): """Create new CU1 gate.""" super().__init__( "cu1", 2, [theta], num_ctrl_qubits=1, label=label, ctrl_state=ctrl_state, base_gate=U1Gate(theta, label=_base_label), duration=duration, unit=unit, ) def _define(self): """ gate cu1(lambda) a,b { u1(lambda/2) a; cx a,b; u1(-lambda/2) b; cx a,b; u1(lambda/2) b; } """ # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit from .x import CXGate # pylint: disable=cyclic-import # ┌─────────┐ # q_0: ┤ U1(λ/2) ├──■────────────────■───────────── # └─────────┘┌─┴─┐┌──────────┐┌─┴─┐┌─────────┐ # q_1: ───────────┤ X ├┤ U1(-λ/2) ├┤ X ├┤ U1(λ/2) ├ # └───┘└──────────┘└───┘└─────────┘ q = QuantumRegister(2, "q") qc = QuantumCircuit(q, name=self.name) rules = [ (U1Gate(self.params[0] / 2), [q[0]], []), (CXGate(), [q[0], q[1]], []), (U1Gate(-self.params[0] / 2), [q[1]], []), (CXGate(), [q[0], q[1]], []), (U1Gate(self.params[0] / 2), [q[1]], []), ] for instr, qargs, cargs in rules: qc._append(instr, qargs, cargs) self.definition = qc def control( self, num_ctrl_qubits: int = 1, label: str | None = None, ctrl_state: str | int | None = None, annotated: bool = False, ): """Controlled version of this 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. Returns: ControlledGate: controlled version of this gate. """ if not annotated and ctrl_state is None: gate = MCU1Gate(self.params[0], num_ctrl_qubits=num_ctrl_qubits + 1, label=label) gate.base_gate.label = self.label else: gate = super().control( num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state, annotated=annotated, ) return gate def inverse(self, annotated: bool = False): r"""Return inverted CU1 gate (:math:`CU1(\lambda)^{\dagger} = CU1(-\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:`.CU1Gate` with inverse parameter values. Returns: CU1Gate: inverse gate. """ return CU1Gate(-self.params[0], ctrl_state=self.ctrl_state) def __array__(self, dtype=None, copy=None): """Return a numpy.array for the CU1 gate.""" if copy is False: raise ValueError("unable to avoid copy while creating an array as requested") eith = exp(1j * float(self.params[0])) if self.ctrl_state: return numpy.array( [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, eith]], dtype=dtype ) else: return numpy.array( [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, eith, 0], [0, 0, 0, 1]], dtype=dtype ) def __eq__(self, other): return ( isinstance(other, CU1Gate) and self.ctrl_state == other.ctrl_state and self._compare_parameters(other) ) class MCU1Gate(ControlledGate): r"""Multi-controlled-U1 gate. This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the state of the control qubits. .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: MCU1(\lambda) = MCP(\lambda) .. code-block:: python circuit = QuantumCircuit(5) circuit.mcp(lambda, list(range(4)), 4) **Circuit symbol:** .. code-block:: text q_0: ────■──── │ . │ q_(n-1): ────■──── ┌───┴───┐ q_n: ┤ U1(λ) ├ └───────┘ .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CU1Gate`: The singly-controlled-version of this gate. """ def __init__( self, lam: ParameterValueType, num_ctrl_qubits: int, label: str | None = None, ctrl_state: str | int | None = None, *, duration=None, unit="dt", _base_label=None, ): """Create new MCU1 gate.""" super().__init__( "mcu1", num_ctrl_qubits + 1, [lam], num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state, base_gate=U1Gate(lam, label=_base_label), duration=duration, unit=unit, ) def _define(self): # pylint: disable=cyclic-import from qiskit.circuit.quantumcircuit import QuantumCircuit q = QuantumRegister(self.num_qubits, "q") qc = QuantumCircuit(q, name=self.name) if self.num_ctrl_qubits == 0: definition = U1Gate(self.params[0]).definition if self.num_ctrl_qubits == 1: definition = CU1Gate(self.params[0]).definition else: from .u3 import _gray_code_chain scaled_lam = self.params[0] / (2 ** (self.num_ctrl_qubits - 1)) bottom_gate = CU1Gate(scaled_lam) definition = _gray_code_chain(q, self.num_ctrl_qubits, bottom_gate) for instr, qargs, cargs in definition: qc._append(instr, qargs, cargs) self.definition = qc def control( self, num_ctrl_qubits: int = 1, label: str | None = None, ctrl_state: str | int | None = None, annotated: bool = False, ): """Controlled version of this 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. Returns: ControlledGate: controlled version of this gate. """ if not annotated: ctrl_state = _ctrl_state_to_int(ctrl_state, num_ctrl_qubits) new_ctrl_state = (self.ctrl_state << num_ctrl_qubits) | ctrl_state gate = MCU1Gate( self.params[0], num_ctrl_qubits=num_ctrl_qubits + self.num_ctrl_qubits, label=label, ctrl_state=new_ctrl_state, ) gate.base_gate.label = self.label else: gate = super().control( num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state, annotated=annotated, ) return gate def inverse(self, annotated: bool = False): r"""Return inverted MCU1 gate (:math:`MCU1(\lambda)^{\dagger} = MCU1(-\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:`.MCU1Gate` with inverse parameter values. Returns: MCU1Gate: inverse gate. """ return MCU1Gate(-self.params[0], self.num_ctrl_qubits) def __eq__(self, other): return ( isinstance(other, MCU1Gate) and self.num_ctrl_qubits == other.num_ctrl_qubits and self.ctrl_state == other.ctrl_state and self._compare_parameters(other) )