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Quantum Machine Learning

Reducing the Complexity of Matrix Multiplication to O\(N^2log_2N\) by an Asymptotically Optimal Quantum Algorithm

arXiv

Authors: Jiaqi Yao, Ding Liu

Year

2026

Paper ID

2809

Status

Preprint

Abstract Read

~2 min

Abstract Words

103

Citations

N/A

Abstract

Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage capacity, offers a potential solution to these limitations. This work presents a quantum kernel-based matrix multiplication algorithm (QKMM) that achieves an asymptotically optimal computational complexity of O\(N² log₂ N\), outperforming the classical optimal complexity of O\(N^2.371552\), where N denotes the matrix dimension. Through noiseless and noisy quantum simulation experiments, we demonstrate that the proposed algorithm not only exhibits superior theoretical efficiency but also shows practical advantages in runtime performance and stability.

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This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
It adds a 2026 reference point for readers tracking recent quantum research.
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.05541 [2] arXiv https://arxiv.org/abs/2602.05541 [3] Publisher https://arxiv.org/abs/2602.05541

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