Abstract <p>In this work, we consider a formulation of the optimal gate generation problem for a fluxonium model of superconducting systems and apply it to the numerical analysis of the corresponding quantum control landscape in a vicinity of the null control. The model includes Schrödinger equation with control and maximization of the objective functionals for gate generation and observable mean value. For a qutrit fluxonium model, the third level can be considered as one of the three computational states. We exploit gradient of the control objective and GRAPE algorithm to perform numerical investigation of the quantum control landscapes for generation of the Hadamard, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8352_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm{T}\)</EquationSource>  </InlineEquation>, and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8352_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm{S}\)</EquationSource>  </InlineEquation> gates and for maximizing mean value of a quantum observable in a vicinity of the null control. The obtained results show high efficiency of gradient-based optimization when it starts from the null control and decrease of the efficiency with increase of the distance of the initial control from the null control for the gate generation problems, and an opposite behaviour for the mean value maximization. For gate generation, the obtained behavior differs (is opposite) from the behavior found previously for maximizing mean value of an observable for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8352_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Lambda\)</EquationSource>  </InlineEquation>-type systems, that may indicate either the absence or low influence of trap at the null control for a fluxonium.</p>

Numerical Analysis of Quantum Control Landscapes for Single-Qubit Gate Generation in Three-Level Fluxonium Systems

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发表日期：

2025年6月1日

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I. M. Korolev,
A. N. Pechen

摘要

Abstract

In this work, we consider a formulation of the optimal gate generation problem for a fluxonium model of superconducting systems and apply it to the numerical analysis of the corresponding quantum control landscape in a vicinity of the null control. The model includes Schrödinger equation with control and maximization of the objective functionals for gate generation and observable mean value. For a qutrit fluxonium model, the third level can be considered as one of the three computational states. We exploit gradient of the control objective and GRAPE algorithm to perform numerical investigation of the quantum control landscapes for generation of the Hadamard, \(\mathrm{T}\) , and \(\mathrm{S}\) gates and for maximizing mean value of a quantum observable in a vicinity of the null control. The obtained results show high efficiency of gradient-based optimization when it starts from the null control and decrease of the efficiency with increase of the distance of the initial control from the null control for the gate generation problems, and an opposite behaviour for the mean value maximization. For gate generation, the obtained behavior differs (is opposite) from the behavior found previously for maximizing mean value of an observable for \(\Lambda\) -type systems, that may indicate either the absence or low influence of trap at the null control for a fluxonium.