量子启发的对角加权矩阵函数解量子化方法：应用于优化随机特征学习
A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features
- The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种量子启发的经典去量子化方法，通过采样重索引和主块缩减，在无采样访问条件下实现优化随机特征采样器的经典化，并保证精度与多项式运行时间。
AI中文摘要：
量子启发的经典算法通过用经典对应物替代量子线性代数子程序，已对若干量子机器学习例程进行了去量子化。然而，基于量子奇异值变换（QSVT）的用于优化随机特征学习的采样器并未被现有的去量子化框架所涵盖，因为待求逆的矩阵本身无法通过采样访问获得。在本工作中，我们开发了一种经典算法来解决这类量子优势候选问题。我们的方法对重索引进行采样，将变换缩减为一个小型主块，并输出具有算子范数保证的稀疏经典表示。应用此方法可对优化随机特征的采样器进行去量子化，从而得到一个具有指定精度和多项式相关运行时间的经典采样器。这些结果表明，量子块编码所依据的分解本身可以提供足够的经典结构，即使复合矩阵的采样和查询访问不可用。
英文摘要：
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.
