Title: Quantum algorithm for the Vlasov equation

Abstract

Typically, the Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution function, we convert the Vlasov-Maxwell system into a Hamiltonian simulation problem. Then for the limiting case of electrostatic Landau damping, we design and verify a quantum algorithm, appropriate for a future error-corrected universal quantum computer. Although the classical simulation has costs that scale as $$\mathcal{O}(N_v t)$$ for a velocity grid with $$N_v$$ grid points and simulation time $$t$$, our quantum algorithm scales as $$\mathcal{O}(\text{polylog}(N_v) t/\delta)$$ where $$\delta$$ is the measurement error, and weaker scalings have been dropped. Extensions, including electromagnetics and higher dimensions, are discussed. A quantum computer could efficiently handle a high-resolution, six-dimensional phase-space grid, but the $$1/\delta$$ cost factor to extract an accurate result remains a difficulty. Our work provides insight into the possibility of someday achieving efficient plasma simulation on a quantum computer.

Authors:

Engel, Alexander  ^[1];

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Smith, Graeme ^[1]; Parker, Scott E. ^[1]

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+ Show Author Affiliations

1. Univ. of Colorado, Boulder, CO (United States)

Publication Date:

Wed Dec 11 00:00:00 EST 2019

Research Org.:

Univ. of Colorado, Boulder, CO (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Fusion Energy Sciences (FES)

OSTI Identifier:

1579923

Grant/Contract Number:  

SC0020393

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review A

Additional Journal Information:

Journal Volume: 100; Journal Issue: 6; Journal ID: ISSN 2469-9926

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS