Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models

• URL: http://arxiv.org/abs/2407.01913v1
• Date: Tue, 2 Jul 2024 03:23:11 GMT
• Title: Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models
• Authors: Shi Jin, Nana Liu,
• Abstract summary: We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations. The key idea is to approximate the heat equations by a system of hyperbolic heat equations that involve only first-order differential operators. For a d-dimensional problem, we show that it is much more appropriate to use a single d-level quantum system - a qudit - instead of its qubit counterpart, and d+1 qumodes.
• Score: 27.193565893837356
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-Scholes and Fokker-Planck equations. The key idea is to approximate the heat equations by a system of hyperbolic heat equations that involve only first-order differential operators. This scheme requires relatively simple interaction terms in the Hamiltonian, which are the electric and magnetic dipole moment-like interaction terms that would be present in a Jaynes-Cummings-like model. For a d-dimensional problem, we show that it is much more appropriate to use a single d-level quantum system - a qudit - instead of its qubit counterpart, and d+1 qumodes. The total resource cost is efficient in d and precision error, and has potential for realisability for instance in cavity and circuit QED systems.

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