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

Apprentissage des EDP pour l’optimisation de portefeuille avec des réseaux de neurones informés par la physique quantique

Letao Wang (), Abdel Lisser (), Sreejith Sreekumar () and Zeno Toffano ()
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Letao Wang: L2S - Laboratoire des signaux et systèmes - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique, CentraleSupélec, Université Paris-Saclay, CNRS - Centre National de la Recherche Scientifique
Abdel Lisser: L2S - Laboratoire des signaux et systèmes - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique, CentraleSupélec, Université Paris-Saclay, CNRS - Centre National de la Recherche Scientifique, Fédération de Mathématiques de CentraleSupélec - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique
Sreejith Sreekumar: L2S - Laboratoire des signaux et systèmes - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique, CentraleSupélec, Université Paris-Saclay
Zeno Toffano: L2S - Laboratoire des signaux et systèmes - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique, CentraleSupélec, Université Paris-Saclay, CNRS - Centre National de la Recherche Scientifique

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Abstract: 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 can be represented as a polynomial that incorporates tensor rank decomposition. Numerical experiments are conducted on the Hamilton--Jacobi--Bellman (HJB) PDE arising from the Merton portfolio optimization problem, which determines the optimal investment fraction between a risky and a risk-free asset. The results show that our quantum models achieve lower losses and approximation errors than a classical fully connected PINN while using substantially fewer trainable parameters. Our quantum models further outperform a classical PINN constructed to share a similar inductive bias, providing experimental evidence of quantum-induced improvement in the tested settings and highlighting a resource-efficient pathway toward classical and near-term quantum solvers for PDEs with exploitable solution structure.

Keywords: Quantum machine learning; Variational quantum algorithm; Quantum Physics-Informed Neural Network; Portfolio optimization; Partial differential equation (search for similar items in EconPapers)
Date: 2026-06-27
Note: View the original document on HAL open archive server: https://hal.science/hal-05407711v3
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