Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation

• URL: http://arxiv.org/abs/2312.09784v3
• Date: Wed, 19 Jun 2024 12:48:43 GMT
• Title: Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation
• Authors: Peter Brearley, Sylvain Laizet,
• Abstract summary: One-dimensional advection can be simulated directly since the central finite difference operator for first-order derivatives is anti-Hermitian. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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