Quantum Algorithm for the Advection-Diffusion Equation with Optimal Success Probability

Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, Thomas Rung.

A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. After discretization, the explicit time-marching operator is separated into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation problem and is combined with the shift operator through the linear combination of unitaries algorithm. The result is an unscaled block encoding of the time-marching operator with an optimal success probability without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time. State-vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings.

Cite as BibTeX

@misc{over2024quantumalgorithmadvectiondiffusionequation,
title={Quantum Algorithm for the Advection-Diffusion Equation with Optimal Success Probability},
author={Paul Over and Sergio Bengoechea and Peter Brearley and Sylvain Laizet and Thomas Rung},
year={2024},
eprint={2410.07909},
archivePrefix={arXiv},
primaryClass={quant-ph},
url={https://arxiv.org/abs/2410.07909},
}

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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.