Scholarlink

<p>Matrix operations are crucial to various computational tasks in various fields, and quantum computing offers a promising avenue to accelerate these operations. We present a quantum matrix multiplication (QMM) algorithm that employs amplitude encoding and combines quantum walks with Chebyshev polynomial approximation to achieve quadratic acceleration for matrix chain multiplication where the same matrix is applied <i>K</i> times while maintaining logarithmic complexity in matrix dimension and precision. The algorithm can be applied to any complex matrix. Furthermore, we discuss integrating our QMM algorithm as a subroutine in other matrix operations and propose strategies to optimize QMM for matrices with large condition numbers with numerical simulation.</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

Faster quantum subroutine for matrix chain multiplication via Chebyshev approximation

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月5日

查看全文
  • Xinying Li,
  • Pei-Lin Zheng,
  • Chengkang Pan,
  • Fei Wang,
  • Chunfeng Cui,
  • Xian Lu

摘要

Matrix operations are crucial to various computational tasks in various fields, and quantum computing offers a promising avenue to accelerate these operations. We present a quantum matrix multiplication (QMM) algorithm that employs amplitude encoding and combines quantum walks with Chebyshev polynomial approximation to achieve quadratic acceleration for matrix chain multiplication where the same matrix is applied K times while maintaining logarithmic complexity in matrix dimension and precision. The algorithm can be applied to any complex matrix. Furthermore, we discuss integrating our QMM algorithm as a subroutine in other matrix operations and propose strategies to optimize QMM for matrices with large condition numbers with numerical simulation.