Abstract
Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. This method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.
| Original language | English |
|---|---|
| Article number | 033806 |
| Journal | AVS Quantum Science |
| Volume | 6 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1 2024 |
Funding
This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. We thank Dr. Jeffrey Yepez for numerous fruitful discussions of this work. S.H.B. acknowledges support from the Georgia Tech Quantum Alliance and a Georgia Tech Seed Grant. E.F.D. acknowledges DOE ASCR funding under the Quantum Computing Application Teams program, FWP No. ERKJ347. This work used Bridges2 at the Pittsburgh Supercomputing Center (PSC) and Delta and the National Center for Supercomputing Applications (NCSA) through Allocation No. PHY210084 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation Grant Nos. 2138259, 2138286, 2138307, 2137603, and 2138296. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC05-00OR22725.