Quantum Worst-Case to Average-Case Reduction for Matrix-Vector Multiplication
Abstract
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.
Cite
@article{arxiv.2510.15721,
title = {Quantum Worst-Case to Average-Case Reduction for Matrix-Vector Multiplication},
author = {Divesh Aggarwal and Dexter Kwan},
journal= {arXiv preprint arXiv:2510.15721},
year = {2025}
}