Quantum Worst-Case to Average-Case Reduction for Matrix-Vector Multiplication

Fuente: arXiv
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Hauptverfasser: Aggarwal, Divesh, Kwan, Dexter
Format: Preprint
Veröffentlicht: 2025
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author Aggarwal, Divesh
Kwan, Dexter
author_facet Aggarwal, Divesh
Kwan, Dexter
contents Worst-case to average-case reductions are a cornerstone of complexity theory, providing a bridge between worst-case hardness and average-case computational difficulty. While recent works have demonstrated such reductions for fundamental problems using deep tools from ad- ditive combinatorics, these approaches often suffer from substantial complexity and suboptimal overheads. In this work, we focus on the quantum setting, and provide a new reduction for the Matrix-Vector Multiplication problem that is more efficient, and conceptually simpler than previous constructions. By adapting hardness self-amplification techniques to the quantum do- main, we obtain a quantum worst-case to average-case reduction with improved dependence on the success probability, laying the groundwork for broader applications in quantum fine-grained complexity.
format Preprint
id arxiv_https___arxiv_org_abs_2510_15721
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantum Worst-Case to Average-Case Reduction for Matrix-Vector Multiplication
Aggarwal, Divesh
Kwan, Dexter
Quantum Physics
Computational Complexity
Data Structures and Algorithms
Worst-case to average-case reductions are a cornerstone of complexity theory, providing a bridge between worst-case hardness and average-case computational difficulty. While recent works have demonstrated such reductions for fundamental problems using deep tools from ad- ditive combinatorics, these approaches often suffer from substantial complexity and suboptimal overheads. In this work, we focus on the quantum setting, and provide a new reduction for the Matrix-Vector Multiplication problem that is more efficient, and conceptually simpler than previous constructions. By adapting hardness self-amplification techniques to the quantum do- main, we obtain a quantum worst-case to average-case reduction with improved dependence on the success probability, laying the groundwork for broader applications in quantum fine-grained complexity.
title Quantum Worst-Case to Average-Case Reduction for Matrix-Vector Multiplication
topic Quantum Physics
Computational Complexity
Data Structures and Algorithms
url https://arxiv.org/abs/2510.15721