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

Ordinary differential equations (ODEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. The study explores a quantuminspired approach to solving ODEs, combining quantum-inspired techniques with classical methods. It focuses on fixed-point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate ODE solutions. Motivated by classical solver limitations, the approach aims to leverage quantum mechanics for innovative problem-solving, exploiting quantum parallelism for faster computations. We expand upon the techniques introduced in [1] 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 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.

REFERENCES

[1] Benjamin Zanger et al. “Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods”. In: Quantum 5 (July 2021), p. 502. ISSN: 2521-327X. DOI: 10 . 22331 / q - 2021 - 07 - 13 - 502. URL: https ://doi.org/10.22331/q-2021-07-13-502.