Quantum Algorithms for Differential Equations in Finance and Physics
- Autores: Javier González Conde
- Directores de la Tesis: Mikel Sanz Ruiz (dir. tes.), Iñigo Luis Egusquiza Egusquiza (tut. tes.)
- Lectura: En la Universidad del País Vasco - Euskal Herriko Unibertsitatea ( España ) en 2025
- Idioma: inglés
- Programa de doctorado: Programa de Doctorado en Física por la Universidad del País Vasco/Euskal Herriko Unibertsitatea
- Menciones:
- Internacional
- Calificación: Sobresaliente Cum Laude
- Materias:
- Enlaces
- Tesis en acceso abierto en: ADDI
- Resumen
In this thesis, we investigate the end-to-end implementation of quantum algorithms for solving differential equations through Hamiltonian simulation, with applications in finance, semi-classical physics, and hardware benchmarking. We particularly focus on the challenge of efficiently loading an initial state into a quantum computer, an area of research that has received limited exploration and whose existing methods have faced scrutiny regarding their robustness and efficiency. This work includes developing advanced techniques for encoding discretized real functions into quantum states and demonstrates how Hamiltonian simulation can be utilized to address the solution of linear partial differential equations through three key examples. These examples illustrate applications ranging from simulating non-Hermitian dynamics in finance to integrating classical Hamiltonian mechanics with quantum mechanics for semi-classical simulations, and introducing time-dependent coefficients for hardware benchmarking. Additionally, it is proposed a novel approach to connect the efficiency of quantum algorithms for nonlinear partial differential equations with physical parameters in fluid dynamics, offering deeper insights about when these algorithms can provide a computational advantage. This thesis establishes a solid foundation for future research and aims to advance the understanding and application of quantum algorithms in solving complex differential equations.
