Sponsor: Sorbonne Université
Context
This work is a direct continuation of Fabrice Serret’s PhD thesis defended in 2024. In the context of Variational Quantum Algorithms (VQAs) for near-term quantum hardware, it was analytically established that the quantum gain with respect to classic computers was negligible, when using Pauli decompositions and QFT for the various energy operators rising from the Gross-Pitaevskii equation.
Objectives
This project aims to investigate if simulations of the time-dependent Gross-Pitaevskii equation may be improved via Trotterisation schemes using the Pauli decomposition method and the relationship between the functional Walsh and Fourier basis developed in the thesis.
References
[1] A. M. Childs and N. Wiebe. Hamiltonian Simulation Using Linear Combinations of Unitary Operations. Quantum Information and Computation, 12(11&12).
[2] E. Kökcü, T. Steckmann, Y. Wang, J. Freericks, E. F. Dumitrescu, and A. F. Kemper. Fixed depth hamiltonian simulation via cartan decomposition. Physical Review Letters, 129(7), Aug. 2022
[2] E. Kökcü, T. Steckmann, Y. Wang, J. Freericks, E. F. Dumitrescu, and A. F.
Kemper. Fixed depth hamiltonian simulation via cartan decomposition. Physical
Review Letters, 129(7), Aug. 2022.
[3] L. Lin. Lecture notes on quantum algorithms for scientific computation, 2022.
[4] M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge Series on Information and the Natural Sciences. Cambridge University Press, 2000.
[5] M. F. Serret. Analysis of variational quantum algorithms for differential equations in the presence of quantum noise : application to the stationary Gross-Pitaevskii equation. Theses, Sorbonne Université, Nov. 2024.