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arXiv · 2312.09784

Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation

Peter Brearley·Sylvain Laizet
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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.

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Peter Brearley, Sylvain Laizet. 2023-12-15. Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation. https://doi.org/10.1103/physreva.110.012430

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