Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection

[2608.27712] Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2608.27712 (quant-ph) [Submitted on 27 Aug 2026] Title: Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection Authors: Mohammad Mehedi Hasan Akash , Turag Dev , Nhat-Quang Nguyen , Yanzhu Chen , Huixuan Wu , Kourosh Shoele View PDF HTML (experimental) 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. Subjects: Quantum Physics (quant-ph) ; Numerical Analysis (math.NA) Cite as: arXiv:2608.27712 [quant-ph] (or arXiv:2608.27712v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.27712 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kourosh Shoele [ view email ] [v1] Thu, 27 Aug 2026 21:00:39 UTC (3,455 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math math.NA References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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. 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