An Improved Method for Quantum Matrix Multiplication

• URL: http://arxiv.org/abs/2311.14044v1
• Date: Thu, 23 Nov 2023 15:00:36 GMT
• Title: An Improved Method for Quantum Matrix Multiplication
• Authors: Nhat A. Nghiem and Tzu-Chieh Wei
• Abstract summary: Following the celebrated quantum algorithm for solving linear equations, we provide an approach to solve a linear system of equations with exponentially improved dependence on precision. A few examples that motivate this application are included and we further discuss an application of this improved matrix application algorithm explicitly with an efficient quantum procedure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with exponentially improved dependence on precision. In this note, we aim to complement such a result for applying a matrix to some quantum state, based upon their Chebyshev polynomial approach. A few examples that motivate this application are included and we further discuss an application of this improved matrix application algorithm explicitly with an efficient quantum procedure.

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