{
  "abstract": "Quantum time-marching algorithms for transport PDEs often represent variable coefficients and forcing through register-expanding dilations, block-encoding oracles, or repeated postselection. We present an alternative algorithm for a forced variable-coefficient advection-diffusion equation in flow-inspired skew-symmetric form that incorporates spatially varying velocity, viscous dissipation, and persistent source injection with a peak logical requirement of $n_q+1$ qubits. A centered skew-symmetric discretization makes the advection operator strictly skew-Hermitian for arbitrary velocity profiles, enabling an ancilla-free unitary realization using a Gray-code Trotter sequence of controlled-$R_y$ rotations. Diffusion is applied in the Fourier basis through a uniformly controlled rotation on one postselected ancilla, which is measured, reset, and reused between the two diffusion half-steps, while the source is incorporated classically through second-order Strang splitting. Statevector simulations for $N=16$ and $32$ recover second-order temporal convergence against high-accuracy classical solutions, while Richardson extrapolation gives fourth-order accuracy and reduces kernel calls by factors of four to fourteen. Independent tests through $N=256$ confirm second-order spatial consistency. We further show that the per-step ancilla failure probability is proportional to the instantaneous viscous dissipation rate, making postselection cost self-regulating over a fifty-fold viscosity range. Stable evolution is demonstrated for $5\\times10^4$ time steps without observable secular error growth, while Gray-code advection accounts for $71$--$95\\%$ of transpiled controlled-NOT gates. The fixed-width kernel provides a qubit-efficient building block for near-term hardware studies, although classical readout and state re-preparation remain the main obstacles to coherent multistep evolution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27712",
  "author_total": 6,
  "authors": [
    {
      "name": "Mohammad Mehedi Hasan Akash"
    },
    {
      "name": "Turag Dev"
    },
    {
      "name": "Nhat-Quang Nguyen"
    },
    {
      "name": "Yanzhu Chen"
    },
    {
      "name": "Huixuan Wu"
    },
    {
      "name": "Kourosh Shoele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cce7ar22vhd4y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27712",
  "fulltext_url": null,
  "id": "cce7ar22vhd4y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27712",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204795878",
  "pdf_url": "https://arxiv.org/pdf/2608.27712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cce7ar22vhd4y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.27712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection",
  "title_text": "Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/cce7ar22vhd4y",
  "venue": "arXiv",
  "versions": []
}