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IEEE International Conference on Quantum Computing and Engineering (QCE)

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

José E. Cruz Serrallés, Oluwadara Ogunkoya, Dog̃a Murat Kürkçüog̃lu, Nicholas Bornman, Norm M. Tubman, Silvia Zorzetti, Riccardo Lattanzi

Published Sep 15, 2024• 0 citations
Publisher

Abstract

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum-inspired techniques with classical methods. It focuses on fixed-point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed-point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

DOI
10.1109/qce60285.2024.00016

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