Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks

Quantum Physics [Submitted on 3 Apr 2026] Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks Letao Wang, Abdel Lisser, Sreejith Sreekumar, Zeno Toffano Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here, we investigate the potential role of quantum circuits for solving PDEs. We design a parameterized quantum circuit (PQC) for implementing a polynomial based on tensor rank decomposition, reducing the quantum resource complexity from exponential to polynomial when the corresponding tensor rank is moderate. Building on this circuit, we develop a Quantum Physics-Informed Neural Network (QPINN) and a Quantum-inspired PINN, both of which guarantee the existence of an approximation of the PDE solution, and this approximation is represented as a polynomial that incorporates tensor rank decomposition. Despite using 80 times fewer parameters in experiments, our quantum models achieve higher accuracy and faster convergence than a classical fully connected PINN when solving the PDE for the Merton portfolio optimization problem, which determines the optimal investment fraction between a risky and a risk-free asset. Our quantum models further outperform a classical PINN constructed to share the same inductive bias, providing experimental evidence of quantum-induced improvement and highlighting a resource-efficient pathway toward classical and near-term quantum PDE solvers. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.03346 [quant-ph]   (or arXiv:2604.03346v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.03346 Focus to learn more Submission history From: Letao Wang [view email] [v1] Fri, 3 Apr 2026 10:24:14 UTC (9,658 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)