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

• URL: http://arxiv.org/abs/2410.07909v1
• Date: Thu, 10 Oct 2024 13:37:08 GMT
• Title: Quantum Algorithm for the Advection-Diffusion Equation with Optimal Success Probability
• Authors: Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, Thomas Rung,
• Abstract summary: The explicit time-marching operator is separated into an advection-like component and a corrective shift operator. The result is an unscaled block encoding of the time-marching operator with an optimal success probability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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