Benchmarking Quantum and Classical Algorithms for the 1D Burgers Equation: QTN, HSE, and PINN
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Quantum Physics arXiv:2602.04239 (quant-ph) [Submitted on 4 Feb 2026] Title:Benchmarking Quantum and Classical Algorithms for the 1D Burgers Equation: QTN, HSE, and PINN Authors:Vanshaj Kerni, Abdelrahman E. Ahmed, Syed Ali Asghar View a PDF of the paper titled Benchmarking Quantum and Classical Algorithms for the 1D Burgers Equation: QTN, HSE, and PINN, by Vanshaj Kerni and 2 other authors View PDF Abstract:We present a comparative benchmark of Quantum Tensor Networks (QTN), the Hydrodynamic Schrödinger Equation (HSE), and Physics-Informed Neural Networks (PINN) for simulating the 1D Burgers' equation. Evaluating these emerging paradigms against classical GMRES and Spectral baselines, we analyse solution accuracy, runtime scaling, and resource overhead across grid resolutions ranging from $N=4$ to $N=128$. Our results reveal a distinct performance hierarchy. The QTN solver achieves superior precision ($L_2 \sim 10^{-7}$) with remarkable near-constant runtime scaling, effectively leveraging entanglement compression to capture shock fronts. In contrast, while the Finite-Difference HSE implementation remains robust, the Spectral HSE method suffers catastrophic numerical instability at high resolutions, diverging significantly at $N=128$. PINNs demonstrate flexibility as mesh-free solvers but stall at lower accuracy tiers ($L_2 \sim 10^{-1}$), limited by spectral bias compared to grid-based methods. Ultimately, while quantum methods offer novel representational advantages for low-resolution fluid dynamics, this study confirms they currently yield no computational advantage over classical solvers without fault tolerance or significant algorithmic breakthroughs in handling non-linear feedback. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.04239 [quant-ph] (or arXiv:2602.04239v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.04239 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vanshaj Kerni [view email] [v1] Wed, 4 Feb 2026 05:57:27 UTC (9,253 KB) Full-text links: Access Paper: View a PDF of the paper titled Benchmarking Quantum and Classical Algorithms for the 1D Burgers Equation: QTN, HSE, and PINN, by Vanshaj Kerni and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)