Quantum-Accelerated Differential Equation Solver

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper presents a novel quantum algorithm designed to accelerate the solution of differential equations. Traditional numerical methods often struggle with the computational complexity of differential equations, particularly for high-dimensional problems. We propose a quantum algorithm that leverages quantum superposition and entanglement to achieve exponential speedups in solution finding, offering a potential paradigm shift in computational capabilities. The core mechanism centers around exploiting quantum superposition to represent multiple solution paths concurrently, dramatically reducing the computational resources required for each solution. We detail the algorithm's design, the theoretical analysis underpinning its performance, and preliminary experimental results demonstrating its efficacy. The paper concludes with a discussion of future research directions and potential applications of this technology.

DOI: 10.5281/zenodo.22278172

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