Trainable Embedding Quantum Physics Informed Neural Networks for Solving Nonlinear PDEs

Trainable Embedding Quantum Physics Informed Neural Networks for Solving Nonlinear PDEs | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Trainable Embedding Quantum Physics Informed Neural Networks for Solving Nonlinear PDEs Stefan Berger, Norbert Hosters, Matthias Möller This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6164042/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 May, 2025 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract This paper proposes a novel approach for solving nonlinear partial differential equations (PDEs) with a quantum computer, the trainable embedding quantum physics informed neural network (TE-QPINN). We combine quantum machine learning (QML) with physics informed neural networks (PINNs) in a hybrid approach. By leveraging the advantages of classical and quantum computers, we can create algorithms that have a potential to be run on noisy intermediate-scale quantum devices (NISQ). We use feedforward neural networks (FNN) as the embedding function, giving the used quantum circuit greater expressibility than previously introduced embedding. This expressibility allows us to solve a wide range of problems without using a problem specific ansatz. In this paper we showcase the capabilities of TE-QPINNs of a wide range of problems, including the two-dimensional Poisson, Burgers and Navier-Stokes equations. In direct comparison with classical PINNs, this approach showed an ability to achieve superior results while using the same number of parameters, highlighting their potential for more efficient optimization in high-dimensional parameter spaces, which could be transformative for future applications. Physical sciences/Mathematics and computing Physical sciences/Mathematics and computing/Computational science Physical sciences/Physics/Quantum physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 May, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 22 Apr, 2025 Reviews received at journal 21 Apr, 2025 Reviews received at journal 11 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers agreed at journal 04 Apr, 2025 Reviewers agreed at journal 02 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Reviewers invited by journal 31 Mar, 2025 Editor assigned by journal 26 Mar, 2025 Submission checks completed at journal 19 Mar, 2025 First submitted to journal 19 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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