Scholarlink

<p>Parameterized quantum circuits (PQCs) are fundamental to many hybrid quantum-classical algorithms. However, existing structure-based optimizers for the training of PQCs, such as Rotosolve and sequential minimal optimization, rely on heuristic node selection or ignore statistical noise, which limits their robustness and accuracy. To address this issue, we propose an interpolation-based coordinate descent (ICD) method as a unified framework for all structure-based optimizers. ICD approximates the cost function through interpolation, recovers its trigonometric structure, and performs global one-dimensional updates on individual parameters. Unlike previous methods, ICD derives optimal interpolation nodes that minimize statistical errors from measurements. For the common case of <i>r</i> equidistant frequencies, we prove that equidistant nodes with spacing 2<i>π</i>/(2<i>r</i>&#xa0;+&#xa0;1) jointly minimize the mean squared error of Fourier coefficient estimates, the condition number of the interpolation matrix, and the average variance of the approximated cost function. Numerical experiments confirm the superior robustness and efficiency of ICD over gradient-based methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Interpolation-based coordinate descent method for parameterized quantum circuits

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月7日

查看全文
  • Zhijian Lai,
  • Jiang Hu,
  • Taehee Ko,
  • Jiayuan Wu,
  • Dong An

摘要

Parameterized quantum circuits (PQCs) are fundamental to many hybrid quantum-classical algorithms. However, existing structure-based optimizers for the training of PQCs, such as Rotosolve and sequential minimal optimization, rely on heuristic node selection or ignore statistical noise, which limits their robustness and accuracy. To address this issue, we propose an interpolation-based coordinate descent (ICD) method as a unified framework for all structure-based optimizers. ICD approximates the cost function through interpolation, recovers its trigonometric structure, and performs global one-dimensional updates on individual parameters. Unlike previous methods, ICD derives optimal interpolation nodes that minimize statistical errors from measurements. For the common case of r equidistant frequencies, we prove that equidistant nodes with spacing 2π/(2r + 1) jointly minimize the mean squared error of Fourier coefficient estimates, the condition number of the interpolation matrix, and the average variance of the approximated cost function. Numerical experiments confirm the superior robustness and efficiency of ICD over gradient-based methods.