Quantum algorithm for the Vlasov equation

Journal Article · 10 December 2019 · Physical Review A

DOI: https://doi.org/10.1103/PhysRevA.100.062315 · OSTI ID:1579923

Engel, Alexander  ^[1]; Smith, Graeme ^[2]; Parker, Scott E. ^[2]

---

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

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.

• Research Organization: Univ. of Colorado, Boulder, CO (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
• Grant/Contract Number: SC0020393
• OSTI ID: 1579923
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 6 Vol. 100; ISSN PLRAAN; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English