Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to leverage the usage of Machine Learning computational frameworks relying on the combined usage of CPUs and co-processors, such as accelerators, to achieve maximum performance. This work investigates the design, implementation, and performance of PINNs, using the Quantum Processing Unit (QPU) co-processor. We design a simple Quantum PINN to solve the one-dimensional Poisson problem using a Continuous Variable (CV) quantum computing framework. We discuss the impact of different optimizers, PINN residual formulation, and quantum neural network depth on the quantum PINN accuracy. We show that the optimizer exploration of the training landscape in the case of quantum PINN is not as effective as in classical PINN, and basic Stochastic Gradient Descent (SGD) optimizers outperform adaptive and high-order optimizers. Finally, we highlight the difference in methods and algorithms between quantum and classical PINNs and outline future research challenges for quantum PINN development.

翻译：物理进化神经网络(PINN)是解决科学计算问题的有力工具,从部分差异等同解决方案到数据同化任务。使用PINN的优势之一是利用机械学习计算框架的使用,依靠CPU和共同处理器(如加速器)的综合使用来实现最大性能。这项工作调查了PINN的设计、实施和性能,使用了量子处理股(QPU)共同处理器。我们设计了一个简单的量子PINN,用一个连续变量量子计算框架解决单维Poisson问题。我们讨论了不同优化器、PINN残余配制和量子神经网络深度对量子 PINN精度的影响。我们表明,在量子 PINN 案例中对培训环境的优化探索不如典型的PINN 和基本的Stochatic Gradigendle(SGD) 优化器超越了适应性和高阶量子优化器。最后,我们强调了SQIN 量子和高级量子研究方法与未来量子研究的差别。