标题： 使用类似Jaynes-Cummings模型的模拟量子模拟抛物型偏微分方程 显示英文标题

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

摘要： 我们提出了一种简化的模拟量子模拟协议，用于制备嵌入抛物型偏微分方程解的量子态，包括热方程、Black-Scholes方程和Fokker-Planck方程。 关键思想是通过仅包含一阶微分算子的双曲热方程系统来近似热方程。 该方案在哈密顿量中需要相对简单的相互作用项，这些项是类似于电和磁偶极矩的相互作用项，这会在类似Jaynes-Cummings的模型中出现。 对于d维问题，我们表明使用单个d级量子系统——一个qudit——而不是其qubit对应物以及d+1个qumodes更为合适。 总资源成本在d和精度误差方面是高效的，并且在腔体和电路QED系统中具有实现的潜力。 显示英文摘要

摘要： 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.