Over, PaulPaulOverBengoechea, SergioSergioBengoecheaBrearley, PeterPeterBrearleyLaizet, SylvainSylvainLaizetRung, ThomasThomasRung2025-07-082025-07-082025-07-01Physical Review A / Atomic, molecular, and optical physics 112 (1): L010401 (2025)https://hdl.handle.net/11420/56144A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic success probability of the squared solution norm without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time. The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State-vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings.en1094-162220251American Physical Society (APS)https://creativecommons.org/licenses/by/4.0/Technology::600: TechnologyJournal Articlehttps://doi.org/10.15480/882.1536810.1103/d8hb-fv9310.15480/882.15368Journal Article