Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation

Quantum Physics arXiv:2609.01904 (quant-ph) [Submitted on 1 Sep 2026] Title:Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation Authors:Tamas Nemeth, Gabor Vattay View a PDF of the paper titled Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation, by Tamas Nemeth and Gabor Vattay View PDF HTML (experimental) Abstract:We present a cohesive framework for simulating seismic wave propagation utilizing quantum computing paradigms and their classical tensor network equivalents. We detail a quantum circuit-based formulation for the explicit finite-difference time-domain (FDTD) solution of the two-dimensional acoustic wave equation and map this quantum architecture onto a tensor train representation, namely for Matrix Product State (MPS). The MPS solver enables deterministic simulation of large-scale wavefield dynamics on classical high-performance computing systems. We demonstrate the MPS representation by computing 2D seismic wavefields on the Marmousi model. Our results indicate that the MPS representation is a viable direction for computing and scaling wavefield propagation. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Software (cs.MS) Cite as: arXiv:2609.01904 [quant-ph] (or arXiv:2609.01904v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.01904 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Gabor Vattay [view email] [v1] Tue, 1 Sep 2026 22:05:17 UTC (494 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation, by Tamas Nemeth and Gabor VattayView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cond-mat cond-mat.dis-nn cs cs.MS 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?) 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?)