Resource Analysis for Quantum Simulation of Spatially Varying Transport-Reaction Equations

Abstract:Spatially varying coefficients are the primary source of circuit complexity in quantum simulation of linear advection-diffusion-reaction equations. This work presents a resource analysis of single-step quantum propagators constructed using sparse FABLE block encodings, Quantum Singular Value Transformation, and linear-combination-of-unitaries. We derive theoretical estimates for qubit count, gate complexity, and circuit depth in terms of the spatial discretization, sparsity, and polynomial degree, and compare these predictions with synthesized quantum circuits for one- and two-dimensional variable-coefficient problems. The resulting analysis quantifies the cost of encoding realistic transport operators and provides practical resource estimates for near-term implementations.

Quantum Physics (quant-ph); Numerical Analysis (math.NA)

arXiv:2608.15827 [quant-ph]

(or arXiv:2608.15827v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.15827 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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