Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows
at moderate Reynolds number
- URL: http://arxiv.org/abs/2310.17973v4
- Date: Tue, 9 Jan 2024 15:17:22 GMT
- Title: Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows
at moderate Reynolds number
- Authors: Claudio Sanavio and Sauro Succi
- Abstract summary: We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method.
We show that, at least for moderate Reynolds numbers between 10 and 100, the Carleman-LB procedure can be successfully truncated at second order.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a quantum computing algorithm for fluid flows based on the
Carleman-linearization of the Lattice Boltzmann (LB) method. First, we
demonstrate the convergence of the classical Carleman procedure at moderate
Reynolds numbers, namely for Kolmogorov-like flows. Then we proceed to
formulate the corresponding quantum algorithm, including the quantum circuit
layout and analyze its computational viability. We show that, at least for
moderate Reynolds numbers between 10 and 100, the Carleman-LB procedure can be
successfully truncated at second order, which is a very encouraging result. We
also show that the quantum circuit implementing the single time-step collision
operator has a fixed depth, regardless of the number of lattice sites. However,
such depth is of the order of ten thousands quantum gates, meaning that quantum
advantage over classical computing is not attainable today, but could be
achieved in the near-mid term future. The same goal for the multi-step version
remains however an open topic for future research.
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