Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator

• URL: http://arxiv.org/abs/2410.07909v2
• Date: Wed, 29 Jan 2025 11:39:42 GMT
• Title: Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator
• Authors: Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, Thomas Rung,
• Abstract summary: A quantum algorithm for simulating multidimensional scalar transport problems is presented. A direct unitary block encoding of the explicit time-marching operator is constructed. The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator.
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• Abstract: A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic success probability of the squared solution norm without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time. The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State-vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings.

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