Related papers: Quantum Circuits for partial differential equations via Schrödingerisation

Quantum Circuits for partial differential equations via Schrödingerisation

URL: http://arxiv.org/abs/2403.10032v2
Date: Sun, 12 May 2024 09:12:57 GMT
Title: Quantum Circuits for partial differential equations via Schrödingerisation
Authors: Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang,
Abstract summary: We present implementation of a quantum algorithm for general PDEs using Schr"odingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme.
Score: 26.7034263292622
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schr\"odinger-type equations. To address this limitation, Schr\"odingerisation techniques have been developed, employing the warped transformation to convert general linear PDEs into Schr\"odinger-type equations. However, despite the development of Schr\"odingerisation techniques, the explicit implementation of the corresponding quantum circuit for solving general PDEs remains to be designed. In this paper, we present detailed implementation of a quantum algorithm for general PDEs using Schr\"odingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme, to demonstrate the effectiveness of our approach. Complexity analysis is also carried out to demonstrate the quantum advantages of these algorithms in high dimensions over their classical counterparts.

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