Physics-informed machine learning is increasingly used in applied scientific computing. Physics-informed neural networks (PINNs) [Raissi19] embed governing physical laws directly into the training objective or model structure, thus enabling the solution of partial differential equations (PDEs) without reliance on predefined meshes. By operating on scattered collocation points, PINNs offer flexibility in handling complex geometries, boundary conditions and inverse problems that are difficult to address with classical discretisation-based methods such as finite element or finite volume schemes.
Motivated by the expressive properties of parameterized quantum circuits (PQCs), several quantum extensions of PINNs, commonly referred to as quantum PINNs (QPINNs), have been proposed [Kyriienko21, Siegl25]. Although research on QPINNs has expanded, most evaluations have focused on simplified or reduced-scale PDE problems, largely due to the current limitations of quantum hardware and simulation capabilities. Consequently, it remains challenging for applied researchers to assess the the practical significance, scalability and performance boundaries of QPINNs.
To address this gap, our work benchmarks QPINNs using a subset of PDEs from the PINNacle benchmark [Hao24], a widely used reference for evaluating classical PINNs. Rather than adapting the benchmark to quantum constraints, we evaluate QPINNs in the original benchmark setting. The objective is to characterize the current performance regime of QPINNs in applied contexts. We identify regimes in which QPINNs achieve performance comparable to classical models, as well as PDEs where performance degrades due to algorithmic, optimization or hardware limitations. Additionally, to advance the practical utility of QPINNs, we incorporate a range of enhancement strategies drawn from recent developments in both classical and quantum literature and demonstrate their effects on model performance.
