Linear Matrix Systems and Quantum Algorithms

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Linear matrix systems represent a fundamental class of problems in mathematics, physics, and engineering, and their efficient solution is crucial for various applications. Traditional methods often rely on computationally intensive algorithms, limiting scalability. This paper explores the potential of leveraging the inherent non-linear properties of linear matrices to design novel quantum algorithms for solving linear systems. We propose a quantum algorithm predicated on the principle that by mapping a linear system into a non-linear representation via a specific matrix transformation, we can achieve speedups that surpass classical approaches. The core mechanism involves constructing a quantum circuit that systematically explores this non-linear space, leveraging quantum phenomena like superposition and entanglement to enhance the search process. The paper details the design of a quantum algorithm for solving linear systems, emphasizing the benefits of this approach and its potential to unlock new possibilities in quantum computation.

DOI: 10.5281/zenodo.22204383

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