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Variational quantum solutions to the advection–diffusion equation for applications in fluid dynamics

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Abstract

Constraints in power consumption and computational power limit the skill of operational numerical weather prediction by classical computing methods. Quantum computing could potentially address both of these challenges. Herein, we present one method to perform fluid dynamics calculations that takes advantage of quantum computing. This hybrid quantum–classical method, which combines several algorithms, scales logarithmically with the dimension of the vector space and quadratically with the number of nonzero terms in the linear combination of unitary operators that specifies the linear operator describing the system of interest. As a demonstration, we apply our method to solve the advection–diffusion equation for a small system using IBM quantum computers. We find that reliable solutions of the equation can be obtained on even the noisy quantum computers available today. This and other methods that exploit quantum computers could replace some of our traditional methods in numerical weather prediction as quantum hardware continues to improve.

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Acknowledgements

RD, DG, CAR, and JDD has been supported by the Office of Naval Research (ONR) through the NRL Base Program, PE 0601153N. We acknowledge quantum computing resources from IBM through a collaboration with the Air Force Research Laboratory (AFRL).

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Authors and Affiliations

  1. National Research Council, Monterey, CA, 93943, USA

    Reuben Demirdjian

  2. Naval Research Laboratory, Washington, DC, 20375, USA

    Daniel Gunlycke

  3. Naval Research Laboratory, Monterey, CA, 93943, USA

    Carolyn A. Reynolds & James D. Doyle

  4. NavAir Warfare Centers –Aircraft Division, Patuxent River, MD, 20770, USA

    Sergio Tafur

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  1. Reuben Demirdjian
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  2. Daniel Gunlycke
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  3. Carolyn A. Reynolds
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Correspondence to Reuben Demirdjian.

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Due to confidentiality agreements, supporting data can only be made available to bona fide researchers subject to a non-disclosure agreement. Details of the data and how to request access are available from Reuben Demirdjian at the U.S. Naval Research Laboratory.

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Demirdjian, R., Gunlycke, D., Reynolds, C.A. et al. Variational quantum solutions to the advection–diffusion equation for applications in fluid dynamics. Quantum Inf Process 21, 322 (2022). https://doi.org/10.1007/s11128-022-03667-7

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