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. While the classical simulation has costs that scale as O(NvT ) for a velocity grid with Nv grid points and simulation time T , our quantum algorithm scales as O(polylog(Nv)T /δ) where δ 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/δ cost factor to extract an accurate result remains a difficulty. This work provides insight into the possibility of someday achieving efficient plasma simulation on a quantum computer.

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

This paper presents the first analysis of Van Allen Probes measurements of the cold plasma density and electric field in the inner magnetosphere to show that intervals of strong modulation at the solar rotation period occur in the locations of the outer plasmasphere and plasmapause (~0.7 R E peak-to-peak), in the large-scale electric field (~0.24 mV/m peak-to-peak), and in the cold plasma density (~250 to~70 cm −3 peak-to-peak). Solar rotation modulation of the inner magnetosphere is more apparent in the declining phase of the solar cycle than near solar maximum. The periodicities in these parameters are compared to solar extreme ultraviolet irradiance, solar wind dawn-dusk electric field, and Kp. The variations in the plasmapause location at the solar rotation period anticorrelate with solar wind electric field, magnetospheric electric field, and Kp, but not with extreme ultraviolet irradiance, indicating that convective erosion is the dominant physical process controlling the plasmapause at these timescales.Plain Language Summary As the Sun rotates with a 27-day period, it also emits winds of ionized gas. In some places these winds are leaving at faster speeds than in other places. These winds flow out to the Earth and beyond, and because the Sun rotates, the Earth is hit with each stream of fast wind every 27 days. A region of cooler ionized gas in space surrounding Earth, called the plasmasphere, shrinks when the effects of the fast wind on Earth's magnetic field cause the removal of the outer part of the plasmasphere. When the wind speeds decrease, the plasmasphere grows in size again. The result is that the plasmasphere breathes in and out at the solar rotation period. We use the Van Allen Probe-B satellite to measure the size and density of the plasmasphere and to show for the first time with direct measurements the 27-day variation in the plasmasphere and its connection to the fast winds from the Sun. This result is important, as the behavior of the plasmasphere affects various kinds of waves that can exist in space around Earth, some of which are responsible for the creation and loss of energetic electrons that can damage spacecraft.

No abstract