Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization. Many problems appearing in science and engineering can be rewritten as a set of differential equations. Quantum algorithms for solving differential equations have shown a provable advantage in the fault-tolerant quantum computing regime, where deep and wide quantum circuits can be used to solve large linear systems like partial differential equations (PDEs) efficiently. Recently, variational approaches to solving non-linear PDEs also with near-term quantum devices were proposed. One of the most promising general approaches is based on recent developments in the field of scientific machine learning for solving PDEs. We extend the applicability of near-term quantum computers to more general scientific machine learning tasks, including the discovery of differential equations from a dataset of measurements. We use differentiable quantum circuits (DQCs) to solve equations parameterized by a library of operators, and perform regression on a combination of data and equations. Our results show a promising path to Quantum Model Discovery (QMoD), on the interface between classical and quantum machine learning approaches. We demonstrate successful parameter inference and equation discovery using QMoD on different systems including a second-order, ordinary differential equation and a non-linear, partial differential equation.
翻译:量子计算法有望加快科学和工程领域一些最具挑战性的问题。提出了量子算法,显示了从化学到物流优化等应用的理论优势。科学和工程领域的许多问题可以重写为一套差异方程式。解决差异方程式的量子计算法在错误容忍量子计算制度中显示出一个可证实的优势,在这个制度中,深海和宽度量子电路可以有效地用于解决诸如部分差异方程(PDEs)等大型线性系统。最近,还提出了解决非线性PDE的非线性PDE的变式方法,并配有近期量子装置。最有希望的一般方法之一是基于科学机器学习领域的最新发展,解决PDEs。我们将近期量子计算机的应用扩大到更普遍的科学机器学习任务,包括从数据集中发现差异方程式。我们使用不同量子电路路路路(DQCs)来解决部分差异参数参数参数参数参数参数,并结合数据和方程式。我们的成果展示了一条很有希望的道路,包括使用普通的等式方方方程式和不同等式等式系统。