Abstract
The development of quantum processors for practical fluid flow problems is a promising yet distant goal. Recent advances in quantum linear solvers have highlighted their potential for classical fluid dynamics. In this study, we evaluate the Harrow-Hassidim-Lloyd (HHL) quantum linear systems algorithm (QLSA) for solving the idealized Hele-Shaw flow. Our focus is on the accuracy and computational cost of the HHL solver, which we find to be sensitive to the condition number, scaling exponentially with problem size. This emphasizes the need for preconditioning to enhance the practical use of QLSAs in fluid flow applications. Moreover, we perform shots-based simulations on quantum simulators and test the HHL solver on superconducting quantum devices, where noise, large circuit depths, and gate errors limit performance. Error suppression and mitigation techniques improve accuracy, suggesting that such fluid flow problems can benchmark noise mitigation efforts. Our findings provide a foundation for future, more complex application of QLSAs in fluid flow simulations.
| Original language | English |
|---|---|
| Article number | 101705 |
| Journal | Physics of Fluids |
| Volume | 36 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 1 2024 |
Funding
The authors thank the insightful discussions with Pooja Rao, Dmitry Lyakh, In-Saeng Suh, and Matt Norman. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy (DOE). The U.S. government retains, and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).