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

Conference · Tue Mar 18 00:00:00 EDT 2025 · No journal information

DOI:https://doi.org/10.2172/2551801· OSTI ID:2551801

Oluwadara, Ogunkoya ^[1]; Cruz Serralles, Jose E. ^[2]; Kurkcuoglu, Doga Murat ^[1]; Bornman, Nicholas ^[1]; Tubman, Norm M. ^[3]; Zorzetti, Silvia ^[1]; Lattanzi, Riccardo

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1. Fermilab
2. New York U.
3. NASA, Ames

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.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); New York U.; NASA, Ames
• Sponsoring Organization: US Department of Energy
• DOE Contract Number: 89243024CSC000002
• OSTI ID: 2551801
• Report Number(s): FERMILAB-SLIDES-25-0043-SQMS; oai:inspirehep.net:2906524
• Resource Type: Conference presentation
• Conference Information: Journal Name: No journal information
• Country of Publication: United States
• Language: English

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