{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09268",
  "author_total": 5,
  "authors": [
    {
      "name": "Nhat-Quang Nguyen"
    },
    {
      "name": "Mohammad Mehedi Hasan Akash"
    },
    {
      "name": "Kourosh Shoele"
    },
    {
      "name": "Yanzhu Chen"
    },
    {
      "name": "Huixuan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bp40afn8x9zg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09268",
  "fulltext_url": null,
  "id": "2bp40afn8x9zg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09268",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7212137538",
  "pdf_url": "https://arxiv.org/pdf/2609.09268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bp40afn8x9zg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09268"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm",
  "title_text": "Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/2bp40afn8x9zg",
  "venue": "arXiv",
  "versions": []
}