Quantum Algorithm For Estimating Eigenvalue

• URL: http://arxiv.org/abs/2211.06179v2
• Date: Tue, 20 Jun 2023 14:39:06 GMT
• Title: Quantum Algorithm For Estimating Eigenvalue
• Authors: Nhat A. Nghiem and Tzu-Chieh Wei
• Abstract summary: We provide a quantum algorithm for estimating the largest eigenvalue in magnitude of a given Hermitian matrix. Our quantum procedure can also yield exponential speedup compared to classical algorithms that solve the same problem.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance these computational tasks, and in some cases, such as solving linear equations, can be shown to yield exponential speedup. Here, employing the techniques in the HHL algorithm and the ideas of the classical power method, we provide a simple quantum algorithm for estimating the largest eigenvalue in magnitude of a given Hermitian matrix. As in the case of the HHL algorithm, our quantum procedure can also yield exponential speedup compared to classical algorithms that solve the same problem. We also discuss a few possible extensions and applications of our quantum algorithm, such as a version of a hybrid quantum-classical Lanczos algorithm.

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