Quantum Circuit Implementation of Two Matrix Product Operations and Elementary Column Transformations
Abstract
This paper focuses on quantum algorithms for three key matrix operations: Hadamard (Schur) product, Kronecker (tensor) product, and elementary column transformations each. By designing specific unitary transformations and auxiliary quantum measurement, efficient quantum schemes with circuit diagrams are proposed. Their computational depths are: O(1) for Kronecker product; O(max(m,n)) for Hadamard product (linked to matrix dimensions); and O(m) for elementary column transformations of (2^n X 2^m) matrices (dependent only on column count).Notably, compared to traditional column transformation via matrix transposition and row transformations, this scheme reduces computation steps and quantum gate usage, lowering quantum computing energy costs.
Cite
@article{arxiv.2511.02413,
title = {Quantum Circuit Implementation of Two Matrix Product Operations and Elementary Column Transformations},
author = {Yu-Hang Liu and Yuan-Hong Tao and Jing-Run Lan and Shao-Ming Fei},
journal= {arXiv preprint arXiv:2511.02413},
year = {2025}
}