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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","","","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(\\lambda) = P(\\lambda)= U(0,0,\\lambda)",""," .. code-block:: python",""," circuit = QuantumCircuit(1)"," circuit.p(lambda, 0) # or circuit.u(0, 0, lambda)","","","",""," **Circuit symbol:**",""," .. parsed-literal::",""," ┌───────┐"," q_0: ┤ U1(λ) ├"," └───────┘",""," **Matrix Representation:**",""," .. math::",""," U1(\\lambda) ="," \\begin{pmatrix}"," 1 & 0 \\\\"," 0 & e^{i\\lambda}"," \\end{pmatrix}",""," **Examples:**",""," .. math::",""," U1(\\lambda = \\pi) = Z",""," .. math::",""," U1(\\lambda = \\pi/2) = S",""," .. math::",""," U1(\\lambda = \\pi/4) = T",""," .. seealso::",""," :class:`~qiskit.circuit.library.standard_gates.RZGate`:"," This gate is equivalent to RZ up to a phase factor.",""," .. math::",""," U1(\\lambda) = e^{i{\\lambda}/2} RZ(\\lambda)",""," :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 `_"," \"\"\"",""," 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 can 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):"," \"\"\"Return a numpy.array for the U1 gate.\"\"\""," lam = float(self.params[0])"," return numpy.array([[1, 0], [0, numpy.exp(1j * lam)]], dtype=dtype)","","","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.",""," **Circuit symbol:**",""," .. parsed-literal::","",""," q_0: ─■──"," │λ"," q_1: ─■──","",""," **Matrix representation:**",""," .. math::",""," CU1(\\lambda) ="," 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\\lambda}"," \\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."," \"\"\"",""," 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 can 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):"," \"\"\"Return a numpy.array for the CU1 gate.\"\"\""," 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"," )","","","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.",""," **Circuit symbol:**",""," .. parsed-literal::",""," 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``. 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