论文标题
用于求解量子计算机上泊松方程的变分量子算法的性能研究
A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer
论文作者
论文摘要
量子计算的最新进展及其增加的可用性导致对可能的应用的兴趣日益增长。其中包括偏微分方程（PDE）的解决方案，例如材料或流量模拟。当前，在短期到短期内有用的量子处理器有用的最有希望的途径是所谓的混合变量量子算法（VQAS）。因此，在嘈杂的中间量表量子（NISQ）时代，已提出了PDE的变异方法作为量子优势的候选。在这项工作中，我们对利用实际量子设备上的VQA进行了广泛的研究来解决PDE的最简单原型 - 泊松方程。尽管对小问题大小的无噪声模拟器的结果似乎很有希望，但量子计算机上的性能非常差。我们认为，通过解决方案的振幅编码PDE的直接分辨率并不是当今量子设备的良好用例，尤其是在考虑大型系统尺寸和更复杂的非线性PDE时，才能与经典的高端求解器竞争。
Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation. Currently, the most promising route to useful deployment of quantum processors in the short to near term are so-called hybrid variational quantum algorithms (VQAs). Thus, variational methods for PDEs have been proposed as a candidate for quantum advantage in the noisy intermediate scale quantum (NISQ) era. In this work, we conduct an extensive study of utilizing VQAs on real quantum devices to solve the simplest prototype of a PDE -- the Poisson equation. Although results on noiseless simulators for small problem sizes may seem deceivingly promising, the performance on quantum computers is very poor. We argue that direct resolution of PDEs via an amplitude encoding of the solution is not a good use case within reach of today's quantum devices -- especially when considering large system sizes and more complicated non-linear PDEs that are required in order to be competitive with classical high-end solvers.
