Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation
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.
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BibTeX
@misc{nemeth2026quantum,
title = {{Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation}},
author = {Tamas Nemeth and Gabor Vattay},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01904},
eprint = {2609.01904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01904},
}
RIS
TY - UNPB
TI - Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation
AU - Tamas Nemeth
AU - Gabor Vattay
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01904
UR - https://arxiv.org/abs/2609.01904
AB - 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.
ER -