A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features

2026-09-09

AI Summary

本文提出一种量子启发的经典算法，通过采样重要索引并转换为小主块，解决基于QSVT的学习优化随机特征无法用现有方法去量化的难题。

Abstract

Quantum-inspired classical algorithms have dequantized several quantum machine learning routines by replacing quantum linear-algebra subroutines with classical counterparts. However, the sampler based on quantum singular value transformation (QSVT) for learning with optimized random features is not covered by existing dequantization frameworks, because the matrix to be inverted is not itself available through sampling access. In this work, we develop a classical algorithm to address this type of quantum-advantage candidate. Our method samples heavy indices, reduces the transformation to a small principal block, and outputs a sparse classical representation with operator-norm guarantees. Applying this method dequantizes the sampler for optimized random features, giving a classical sampler with prescribed accuracy and polynomially related runtime. These results show that the factorization underlying a quantum block encoding can itself provide sufficient classical structure even when sampling-and-query access to the composite matrix is unavailable.

Problem

• Quantum-inspired
• Dequantization
• Random Features
• Singular Value Transformation
• Classical Algorithm

Innovation

• Quantum-inspired classical algorithm
• Diagonally weighted matrix functions
• Optimized random features
• Dequantization