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

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.

Authors 3

Natsuto Isogai, Mio Murao, Hayata Yamasaki

Specification

Official page: arxiv.org/abs/2609.10729
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
arXiv id: 2609.10729
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Categories: quant-ph, cs.LG, stat.ML
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
PDF: arxiv.org/pdf/2609.10729
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Primary category: quant-ph
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh

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9

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T19

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6 h ago

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Authors: Natsuto Isogai, Mio Murao, Hayata Yamasaki

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Claim history · Official page

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Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2609.10729	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperA Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features
New paper: A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features
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Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	5 h ago	1

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