Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Journal Article · 19 September 2024 · AVS Quantum Science

DOI: https://doi.org/10.1116/5.0217675 · OSTI ID:2472732

Kocherla, Sriharsha  ^[1]; Song, Zhixin  ^[1]; Chrit, Fatima Ezahra  ^[1]; Gard, Bryan  ^[2]; Dumitrescu, Eugene F.  ^[3]; Alexeev, Alexander  ^[1]; Bryngelson, Spencer H.  ^[1]

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1. Georgia Institute of Technology, Atlanta, GA (United States)
2. Georgia Inst. of Technology, Atlanta, GA (United States). Georgia Tech Research Institute
3. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

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. Further, 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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
• Sponsoring Organization: National Science Foundation; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 2472732
• Journal Information: AVS Quantum Science, Journal Name: AVS Quantum Science Journal Issue: 3 Vol. 6; ISSN 2639-0213
• Publisher: American Institute of Physics (AIP) - American Vacuum SocietyCopyright Statement
• Country of Publication: United States
• Language: English