Quantum simulation of partial differential equations via Schrodingerisation

• URL: http://arxiv.org/abs/2212.13969v1
• Date: Wed, 28 Dec 2022 17:32:38 GMT
• Title: Quantum simulation of partial differential equations via Schrodingerisation
• Authors: Shi Jin, Nana Liu and Yue Yu
• Abstract summary: We present a simple new way to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations. This can be seen directly on the level of the dynamical equations without more sophisticated methods.
• Score: 31.986350313948435
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations - in real time - in a straightforward way. This can be seen directly on the level of the dynamical equations without more sophisticated methods. This approach is not only applicable to PDEs for classical problems but also those for quantum problems - like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit.

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