References & Citations
Quantum Physics
Title: Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation
(Submitted on 15 Dec 2023 (v1), last revised 25 Apr 2024 (this version, v2))
Abstract: A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference operator for first-order derivatives is anti-Hermitian. Here, this is extended to industrially relevant, multi-dimensional flows with realistic boundary conditions and arbitrary finite difference stencils. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps, the sparsity of the time-marching operator and the inverse of the allowable error. Statevector simulations of a scalar transported in a two-dimensional channel flow and lid-driven cavity configuration are presented as a proof of concept of the proposed approach.
Submission history
From: Peter Brearley [view email][v1] Fri, 15 Dec 2023 13:39:27 GMT (3172kb,D)
[v2] Thu, 25 Apr 2024 10:45:27 GMT (8048kb,D)
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