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This code is part of Qiskit.","#","# (C) Copyright IBM 2018, 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.","\"\"\"","Multiple-Controlled U3 gate. Not using ancillary qubits.","\"\"\"","","from math import pi","from typing import Optional, Union, Tuple, List","import numpy as np","","from qiskit.circuit import QuantumCircuit, QuantumRegister, Qubit","from qiskit.circuit.library.standard_gates.x import MCXGate","from qiskit.circuit.library.standard_gates.u3 import _generate_gray_code","from qiskit.circuit.parameterexpression import ParameterValueType","from qiskit.exceptions import QiskitError","","","def _apply_cu(circuit, theta, phi, lam, control, target, use_basis_gates=True):"," if use_basis_gates:"," # pylint: disable=cyclic-import"," # ┌──────────────┐"," # control: ┤ P(λ/2 + φ/2) ├──■──────────────────────────────────■────────────────"," # ├──────────────┤┌─┴─┐┌────────────────────────────┐┌─┴─┐┌────────────┐"," # target: ┤ P(λ/2 - φ/2) ├┤ X ├┤ U(-0.5*0,0,-0.5*λ - 0.5*φ) ├┤ X ├┤ U(0/2,φ,0) ├"," # └──────────────┘└───┘└────────────────────────────┘└───┘└────────────┘"," circuit.p((lam + phi) / 2, [control])"," circuit.p((lam - phi) / 2, [target])"," circuit.cx(control, target)"," circuit.u(-theta / 2, 0, -(phi + lam) / 2, [target])"," circuit.cx(control, target)"," circuit.u(theta / 2, phi, 0, [target])"," else:"," circuit.cu(theta, phi, lam, 0, control, target)","","","def _apply_mcu_graycode(circuit, theta, phi, lam, ctls, tgt, use_basis_gates):"," \"\"\"Apply multi-controlled u gate from ctls to tgt using graycode"," pattern with single-step angles theta, phi, lam.\"\"\"",""," n = len(ctls)",""," gray_code = _generate_gray_code(n)"," 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:"," circuit.cx(ctls[pos], ctls[lm_pos])"," else:"," indices = [i for i, x in enumerate(pattern) if x == \"1\"]"," for idx in indices[1:]:"," circuit.cx(ctls[idx], ctls[lm_pos])"," # check parity and undo rotation"," if pattern.count(\"1\") % 2 == 0:"," # inverse CU: u(theta, phi, lamb)^dagger = u(-theta, -lam, -phi)"," _apply_cu("," circuit, -theta, -lam, -phi, ctls[lm_pos], tgt, use_basis_gates=use_basis_gates"," )"," else:"," _apply_cu(circuit, theta, phi, lam, ctls[lm_pos], tgt, use_basis_gates=use_basis_gates)"," last_pattern = pattern","","","def _mcsu2_real_diagonal("," unitary: np.ndarray,"," num_controls: int,"," ctrl_state: Optional[str] = None,"," use_basis_gates: bool = False,",") -> QuantumCircuit:"," \"\"\""," Return a multi-controlled SU(2) gate [1]_ with a real main diagonal or secondary diagonal.",""," Args:"," unitary: SU(2) unitary matrix with one real diagonal."," num_controls: The number of control qubits."," ctrl_state: The state on which the SU(2) operation is controlled. Defaults to all"," control qubits being in state 1."," use_basis_gates: If ``True``, use ``[p, u, cx]`` gates to implement the decomposition.",""," Returns:"," A :class:`.QuantumCircuit` implementing the multi-controlled SU(2) gate.",""," Raises:"," QiskitError: If the input matrix is invalid.",""," References:",""," .. [1]: R. Vale et al. Decomposition of Multi-controlled Special Unitary Single-Qubit Gates"," `arXiv:2302.06377 (2023) `__",""," \"\"\""," # pylint: disable=cyclic-import"," from .x import MCXVChain"," from qiskit.circuit.library.generalized_gates import UnitaryGate"," from qiskit.quantum_info.operators.predicates import is_unitary_matrix"," from qiskit.compiler import transpile",""," if unitary.shape != (2, 2):"," raise QiskitError(f\"The unitary must be a 2x2 matrix, but has shape {unitary.shape}.\")",""," if not is_unitary_matrix(unitary):"," raise QiskitError(f\"The unitary in must be an unitary matrix, but is {unitary}.\")",""," if not np.isclose(1.0, np.linalg.det(unitary)):"," raise QiskitError(\"Invalid Value _mcsu2_real_diagonal requires det(unitary) equal to one.\")",""," is_main_diag_real = np.isclose(unitary[0, 0].imag, 0.0) and np.isclose(unitary[1, 1].imag, 0.0)"," is_secondary_diag_real = np.isclose(unitary[0, 1].imag, 0.0) and np.isclose("," unitary[1, 0].imag, 0.0"," )",""," if not is_main_diag_real and not is_secondary_diag_real:"," raise QiskitError(\"The unitary must have one real diagonal.\")",""," if is_secondary_diag_real:"," x = unitary[0, 1]"," z = unitary[1, 1]"," else:"," x = -unitary[0, 1].real"," z = unitary[1, 1] - unitary[0, 1].imag * 1.0j",""," if np.isclose(z, -1):"," s_op = [[1.0, 0.0], [0.0, 1.0j]]"," else:"," alpha_r = np.sqrt((np.sqrt((z.real + 1.0) / 2.0) + 1.0) / 2.0)"," alpha_i = z.imag / (2.0 * np.sqrt((z.real + 1.0) * (np.sqrt((z.real + 1.0) / 2.0) + 1.0)))"," alpha = alpha_r + 1.0j * alpha_i"," beta = x / (2.0 * np.sqrt((z.real + 1.0) * (np.sqrt((z.real + 1.0) / 2.0) + 1.0)))",""," # S gate definition"," s_op = np.array([[alpha, -np.conj(beta)], [beta, np.conj(alpha)]])",""," s_gate = UnitaryGate(s_op)",""," k_1 = int(np.ceil(num_controls / 2.0))"," k_2 = int(np.floor(num_controls / 2.0))",""," ctrl_state_k_1 = None"," ctrl_state_k_2 = None",""," if ctrl_state is not None:"," str_ctrl_state = f\"{ctrl_state:0{num_controls}b}\""," ctrl_state_k_1 = str_ctrl_state[::-1][:k_1][::-1]"," ctrl_state_k_2 = str_ctrl_state[::-1][k_1:][::-1]",""," circuit = QuantumCircuit(num_controls + 1, name=\"MCSU2\")"," controls = list(range(num_controls)) # control indices, defined for code legibility"," target = num_controls # target index, defined for code legibility",""," if not is_secondary_diag_real:"," circuit.h(target)",""," mcx_1 = MCXVChain(num_ctrl_qubits=k_1, dirty_ancillas=True, ctrl_state=ctrl_state_k_1)"," circuit.append(mcx_1, controls[:k_1] + [target] + controls[k_1 : 2 * k_1 - 2])"," circuit.append(s_gate, [target])",""," mcx_2 = MCXVChain("," num_ctrl_qubits=k_2,"," dirty_ancillas=True,"," ctrl_state=ctrl_state_k_2,"," # action_only=general_su2_optimization # Requires PR #9687"," )"," circuit.append(mcx_2.inverse(), controls[k_1:] + [target] + controls[k_1 - k_2 + 2 : k_1])"," circuit.append(s_gate.inverse(), [target])",""," mcx_3 = MCXVChain(num_ctrl_qubits=k_1, dirty_ancillas=True, ctrl_state=ctrl_state_k_1)"," circuit.append(mcx_3, controls[:k_1] + [target] + controls[k_1 : 2 * k_1 - 2])"," circuit.append(s_gate, [target])",""," mcx_4 = MCXVChain(num_ctrl_qubits=k_2, dirty_ancillas=True, ctrl_state=ctrl_state_k_2)"," circuit.append(mcx_4, controls[k_1:] + [target] + controls[k_1 - k_2 + 2 : k_1])"," circuit.append(s_gate.inverse(), [target])",""," if not is_secondary_diag_real:"," circuit.h(target)",""," if use_basis_gates:"," circuit = transpile(circuit, basis_gates=[\"p\", \"u\", \"cx\"])",""," return circuit","","","def mcrx("," self,"," theta: ParameterValueType,"," q_controls: Union[QuantumRegister, List[Qubit]],"," q_target: Qubit,"," use_basis_gates: bool = False,","):"," \"\"\""," Apply Multiple-Controlled X rotation gate",""," Args:"," self (QuantumCircuit): The QuantumCircuit object to apply the mcrx gate on."," theta (float): angle theta"," q_controls (QuantumRegister or list(Qubit)): The list of control qubits"," q_target (Qubit): The target qubit"," use_basis_gates (bool): use p, u, cx",""," Raises:"," QiskitError: parameter errors"," \"\"\""," from .rx import RXGate",""," control_qubits = self.qbit_argument_conversion(q_controls)"," target_qubit = self.qbit_argument_conversion(q_target)"," if len(target_qubit) != 1:"," raise QiskitError(\"The mcrz gate needs a single qubit as target.\")"," all_qubits = control_qubits + target_qubit"," target_qubit = target_qubit[0]"," self._check_dups(all_qubits)",""," n_c = len(control_qubits)"," if n_c == 1: # cu"," _apply_cu("," self,"," theta,"," -pi / 2,"," pi / 2,"," control_qubits[0],"," target_qubit,"," use_basis_gates=use_basis_gates,"," )"," elif n_c < 4:"," theta_step = theta * (1 / (2 ** (n_c - 1)))"," _apply_mcu_graycode("," self,"," theta_step,"," -pi / 2,"," pi / 2,"," control_qubits,"," target_qubit,"," use_basis_gates=use_basis_gates,"," )"," else:"," cgate = _mcsu2_real_diagonal("," RXGate(theta).to_matrix(),"," num_controls=len(control_qubits),"," use_basis_gates=use_basis_gates,"," )"," self.compose(cgate, control_qubits + [target_qubit], inplace=True)","","","def mcry("," self,"," theta: ParameterValueType,"," q_controls: Union[QuantumRegister, List[Qubit]],"," q_target: Qubit,"," q_ancillae: Optional[Union[QuantumRegister, Tuple[QuantumRegister, int]]] = None,"," mode: str = None,"," use_basis_gates=False,","):"," \"\"\""," Apply Multiple-Controlled Y rotation gate",""," Args:"," self (QuantumCircuit): The QuantumCircuit object to apply the mcry gate on."," theta (float): angle theta"," q_controls (list(Qubit)): The list of control qubits"," q_target (Qubit): The target qubit"," q_ancillae (QuantumRegister or tuple(QuantumRegister, int)): The list of ancillary qubits."," mode (string): The implementation mode to use"," use_basis_gates (bool): use p, u, cx",""," Raises:"," QiskitError: parameter errors"," \"\"\""," from .ry import RYGate",""," control_qubits = self.qbit_argument_conversion(q_controls)"," target_qubit = self.qbit_argument_conversion(q_target)"," if len(target_qubit) != 1:"," raise QiskitError(\"The mcrz gate needs a single qubit as target.\")"," ancillary_qubits = [] if q_ancillae is None else self.qbit_argument_conversion(q_ancillae)"," all_qubits = control_qubits + target_qubit + ancillary_qubits"," target_qubit = target_qubit[0]"," self._check_dups(all_qubits)",""," # auto-select the best mode"," if mode is None:"," # if enough ancillary qubits are provided, use the 'v-chain' method"," additional_vchain = MCXGate.get_num_ancilla_qubits(len(control_qubits), \"v-chain\")"," if len(ancillary_qubits) >= additional_vchain:"," mode = \"basic\""," else:"," mode = \"noancilla\"",""," if mode == \"basic\":"," self.ry(theta / 2, q_target)"," self.mcx(q_controls, q_target, q_ancillae, mode=\"v-chain\")"," self.ry(-theta / 2, q_target)"," self.mcx(q_controls, q_target, q_ancillae, mode=\"v-chain\")"," elif mode == \"noancilla\":"," n_c = len(control_qubits)"," if n_c == 1: # cu"," _apply_cu("," self, theta, 0, 0, control_qubits[0], 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