Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm
Abstract
Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto--Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics.
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BibTeX
@misc{nguyen2026reconstructing,
title = {{Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm}},
author = {Nhat-Quang Nguyen and Mohammad Mehedi Hasan Akash and Kourosh Shoele and Yanzhu Chen and Huixuan Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09268},
eprint = {2609.09268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm
AU - Nhat-Quang Nguyen
AU - Mohammad Mehedi Hasan Akash
AU - Kourosh Shoele
AU - Yanzhu Chen
AU - Huixuan Wu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09268
UR - https://arxiv.org/abs/2609.09268
AB - Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto--Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics.
ER -