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.
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September 2024
Research Article|
September 20 2024
Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations
Sriharsha Kocherla
;
Sriharsha Kocherla
(Conceptualization, Data curation, Methodology, Software, Validation, Writing – original draft)
1
School of Computational Science and Engineering, Georgia Institute of Technology
, Atlanta, Georgia 30332
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Zhixin Song
;
Zhixin Song
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft)
2
School of Physics, Georgia Institute of Technology
, Atlanta, Georgia 30332
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Fatima Ezahra Chrit
;
Fatima Ezahra Chrit
(Conceptualization, Formal analysis, Investigation, Methodology, Software)
1
School of Computational Science and Engineering, Georgia Institute of Technology
, Atlanta, Georgia 303323
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology
, Atlanta, Georgia 30332
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Bryan Gard
;
Bryan Gard
(Formal analysis, Investigation, Methodology, Resources)
4
CIPHER, Georgia Tech Research Institute
, Atlanta, Georgia 30332
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Eugene F. Dumitrescu
;
Eugene F. Dumitrescu
(Formal analysis, Investigation, Methodology, Project administration, Software)
5
Oak Ridge National Laboratory
, Oak Ridge, Tennessee 37830
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Alexander Alexeev
;
Alexander Alexeev
(Conceptualization, Funding acquisition, Methodology, Project administration, Supervision, Writing – original draft)
3
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology
, Atlanta, Georgia 30332
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Spencer H. Bryngelson
Spencer H. Bryngelson
a)
(Conceptualization, Funding acquisition, Investigation, Methodology, Supervision, Validation, Visualization, Writing – original draft)
1
School of Computational Science and Engineering, Georgia Institute of Technology
, Atlanta, Georgia 303323
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology
, Atlanta, Georgia 303326
Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology
, Atlanta, Georgia 30332 a)Author to whom correspondence should be addressed: shb@gatech.edu
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a)Author to whom correspondence should be addressed: shb@gatech.edu
AVS Quantum Sci. 6, 033806 (2024)
Article history
Received:
May 06 2024
Accepted:
August 28 2024
Citation
Sriharsha Kocherla, Zhixin Song, Fatima Ezahra Chrit, Bryan Gard, Eugene F. Dumitrescu, Alexander Alexeev, Spencer H. Bryngelson; Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations. AVS Quantum Sci. 1 September 2024; 6 (3): 033806. https://doi.org/10.1116/5.0217675
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