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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2020.","#","# 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.","","\"\"\"The Random Pauli circuit class.\"\"\"","","from __future__ import annotations","import numpy as np","","from qiskit.circuit import QuantumCircuit","","","from .two_local import TwoLocal","","","class PauliTwoDesign(TwoLocal):"," r\"\"\"The Pauli Two-Design ansatz.",""," This class implements a particular form of a 2-design circuit [1], which is frequently studied"," in quantum machine learning literature, such as e.g. the investigating of Barren plateaus in"," variational algorithms [2].",""," The circuit consists of alternating rotation and entanglement layers with"," an initial layer of :math:`\\sqrt{H} = RY(\\pi/4)` gates."," The rotation layers contain single qubit Pauli rotations, where the axis is chosen uniformly"," at random to be X, Y or Z. The entanglement layers is compromised of pairwise CZ gates"," with a total depth of 2.",""," For instance, the circuit could look like this (but note that choosing a different seed"," yields different Pauli rotations).",""," .. parsed-literal::",""," ┌─────────┐┌──────────┐ ░ ┌──────────┐ ░ ┌──────────┐"," q_0: ┤ RY(π/4) ├┤ RZ(θ[0]) ├─■─────░─┤ RY(θ[4]) ├─■─────░──┤ RZ(θ[8]) ├"," ├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ├──────────┤"," q_1: ┤ RY(π/4) ├┤ RZ(θ[1]) ├─■──■──░─┤ RY(θ[5]) ├─■──■──░──┤ RX(θ[9]) ├"," ├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ┌┴──────────┤"," q_2: ┤ RY(π/4) ├┤ RX(θ[2]) ├─■──■──░─┤ RY(θ[6]) ├─■──■──░─┤ RX(θ[10]) ├"," ├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ├───────────┤"," q_3: ┤ RY(π/4) ├┤ RZ(θ[3]) ├─■─────░─┤ RX(θ[7]) ├─■─────░─┤ RY(θ[11]) ├"," └─────────┘└──────────┘ ░ └──────────┘ ░ └───────────┘",""," Examples:",""," .. plot::"," :include-source:",""," from qiskit.circuit.library import PauliTwoDesign"," circuit = PauliTwoDesign(4, reps=2, seed=5, insert_barriers=True)"," circuit.draw('mpl')",""," References:",""," [1]: Nakata et al., Unitary 2-designs from random X- and Z-diagonal unitaries."," `arXiv:1502.07514 `_",""," [2]: McClean et al., Barren plateaus in quantum neural network training landscapes."," `arXiv:1803.11173 `_"," \"\"\"",""," def __init__("," self,"," num_qubits: int | None = None,"," reps: int = 3,"," seed: int | None = None,"," insert_barriers: bool = False,"," name: str = \"PauliTwoDesign\","," ):"," \"\"\""," Args:"," num_qubits: The number of qubits of the Pauli Two-Design circuit."," reps: Specifies how often a block consisting of a rotation layer and entanglement"," layer is repeated."," seed: The seed for randomly choosing the axes of the Pauli rotations."," insert_barriers: If ``True``, barriers are inserted in between each layer. 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