April 15-17

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Author: Alexander G. Engel
Requested Type: Poster
Submitted: 2019-02-22 16:03:03

Co-authors: Scott Parker, Graeme Smith

Contact Info:
University of Colorado
2000 Colorado Ave
Boulder, Colorado   80309
United States

Abstract Text:
Kinetic plasma simulations often push the limits of the largest available supercomputers. Meanwhile, in the field of quantum computing, algorithms are being developed that offer a variety of improvements in computational complexity over their classical counterparts (e.g. [1], [2]). The question arises whether quantum computers could be applied to reduce the costs of plasma simulations. We take a small step in this direction by developing an algorithm for a very simple plasma problem: linear Landau damping. This algorithm, which is designed to be run on a universal, error-corrected quantum computer, is worked out in detail and verified numerically. Compared to a classical simulation of the Vlasov-Poisson system, we get an exponential speedup with respect to the velocity grid size in exchange for an extra cost associated with measurement. Therefore, a high resolution, three-dimensional velocity space grid is practically free, but extracting an accurate result adds a cost factor scaling inversely with the error. With this as a concrete example, we discuss the challenges of applying quantum computing to large-scale simulation problems in general. Of particular importance is the challenge of nonlinearity. While quantum logic is always linear and unitary, a limited amount of nonlinearity or non-unitarity can still be efficiently simulated by a quantum computer. This suggests some strategies, which we begin to explore, that might permit quantum speedups for nonlinear problems. One is the application of homotopy analysis method [3] to approximate solutions to nonlinear differential equations. This requires only low-degree polynomials of the input data, and that kind of nonlinearity can be handled by a quantum algorithm, so a speedup over the classical version remains a possibility.

[1] L. K. Grover. Phys. Rev. Lett. 79 325 (1997).
[2] A. W. Harrow, A. Hassidim, and S. Lloyd. Phys. Rev. Lett. 103.15 150502 (2009).
[3] S.J. Liao. Int. J. Non-Linear Mech. 30 371 (1995).

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