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arXiv · 2511.02413

Quantum Circuit Implementation of Two Matrix Product Operations and Elementary Column Transformations

Yu-Hang Liu·Yuan-Hong Tao·Jing-Run Lan·Shao-Ming Fei
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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.

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Yu-Hang Liu, Yuan-Hong Tao, Jing-Run Lan, Shao-Ming Fei. 2025-11-04. Quantum Circuit Implementation of Two Matrix Product Operations and Elementary Column Transformations. https://arxiv.org/abs/2511.02413

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