A Survey of Quantum Computing for PDEs

February 22, 2022, 10:00 a.m. (CET)

by Prof. Dr. Matthias Möller, TU Delft

Time: February 22, 2022, 10:00 a.m. (CET)
  Hybrid event: Send email to dominik.goeddeke@mathematik.uni-stuttgart.de to reserve on-site participation (30 people max on-site)
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Join us via https://unistuttgart.webex.com/unistuttgart/j.php?MTID=m1b4108a825e8a036e305a4cf7dc59af6.

Quantum computing (QC) is an emerging technology that has the potential to radically change the way we will be solving computational problems in the future. While today's Noisy Intermediate-Scale Quantum (NISQ) computers have severe limitations, full-fledged QC systems that surpass the computational capabilities of classical computers are expected within this decade.

In this talk, I will give an overview of quantum algorithms and quantum-assisted computational methods for PDEs. Starting with the well-known HHL algorithm [1] and its various variants, we will discuss the fine-prints of its application to systems that arise from the discretization of PDEs with classical numerical methods. The second part of the talk will focus on hybrid classical-quantum algorithms, in particular, the variational quantum linear solver proposed by Bravo-Prieto et al. [2]. The third part of the talk will give a brief overview of unconventional approaches such as [3].

 

[1] A.W. Harrow, A. Hassidim, and S. Lloyd (2008): Quantum algorithm
    for solving linear systems of equations". Physical Review
    Letters. 103 (15): 150502.

[2] C. Bravo-Prieto, R. LaRose, M. Cerezo, Y. Subasi, L. Cincio, and
    P.J. Coles (2019): Variational Quantum Linear Solver. arXiv:1909.05820

[3] F. Gaitan (2020): Finding flows of a Navier–Stokes fluid through
    quantum computing. npj Quantum Inf 6, 61

[4] R. Steijl (2019): Quantum Algorithms for Fluid Simulations. In:
    Bulnes, F. (ed.) Advances in Quantum Communication and
    Information. IntechOpen. ISBN 9781789852684

[Picture: © Bildagentur PantherMedia / welcomia]

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