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

Conference · Sun Sep 15 00:00:00 EDT 2024 · No journal information

DOI:https://doi.org/10.1109/QCE60285.2024.00016· OSTI ID:2477307

Serrallés, José Cruz ^[1]; Ogunkoya, Oluwadara ^[2]; Kürkçüog̃lu, Dog̃a Murat ^[2]; Bornman, Nicholas ^[2]; Tubman, Norm M. ^[3]; Zorzetti, Silvia ^[2]; Lattanzi, Riccardo ^[1]

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1. New York U.
2. Fermilab
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: NASA, Ames; Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); New York U.
• Sponsoring Organization: US Department of Energy
• DOE Contract Number: AC02-07CH11359; 89243024CSC000002
• OSTI ID: 2477307
• Report Number(s): FERMILAB-CONF-24-0195-SQMS; oai:inspirehep.net:2848236
• Resource Type: Conference paper
• Conference Information: Journal Name: No journal information
• Country of Publication: United States
• Language: English

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