On applications of quantum computing to plasma simulations

Abstract

Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is traditionally aimed at modeling linear Hamiltonian systems of a particular form that is found in quantum mechanics, so extending the existing results to plasma applications remains a challenge. Here, we report a preliminary exploration of the long-term opportunities and likely obstacles in this area. First, we show that many plasma-wave problems are naturally representable in a quantumlike form and thus are naturally fit for quantum computers. Second, we consider more general plasma problems that include non-Hermitian dynamics (instabilities, irreversible dissipation) and nonlinearities. We show that by extending the configuration space, such systems can also be represented in a quantumlike form and thus can be simulated with quantum computers too, albeit that requires more computational resources compared to the first case. Third, we outline potential applications of hybrid quantum-classical computers, which include analysis of global eigenmodes and also an alternative approach to nonlinear simulations.

Improved quantum algorithms for linear and nonlinear differential equations

“…Other works that address aspects of differential equations but with an application to plasma physics are [19], where a quantum algorithm to solve a linearized Vlasov equation is given. In [20,21], a formulation of several interesting problems in plasma physics that could be amenable to quantum algorithms through linearization is given and in [22], a quantum algorithm to solve classical dynamics using the Koopman operator approach is given. In [23], a quantum algorithm to solve cold plasma waves is given.…”

Quantum algorithm for nonlinear differential equations

“…Note that this issue also arises for the quantum solution of linear equations when the governing matrix has eigenvalues with positive real part. In both the linear and the nonlinear cases, the quantum solution gives an exponential speed up only over times where such amplification does not result in violations of equation (19).…”

“…Other efforts to present quantum algorithms for nonlinear differential equations rely on variational techniques [18], but do not supply the provable exponential speed-up given by our algorithm. A separate method involves the Madelung hydrodynamic approach to quantum mechanics [19]. A recently posted work [20] presents a method similar to that pursued here, using a linear system over multiple copies to induce the single-system nonlinearity and applying the quantum linear differential equation solver, but uses classical Carleman linearization instead of the quantum nonlinear Schrödinger linearization technique.…”

Koopman wavefunctions and Clebsch variables in Vlasov-Maxwell kinetic theory

“…Ongoing discussions [41] on the potential of quantum information and computation in plasma physics have recently led to exploiting Hilbert-space approaches in the numerical simulation of magnetized plasmas [15,27,14,16], of the Navier-Stokes equations [19], and of arbitrary non-Hamiltonian systems of equations [27,31]. In particular, recent work [27] has emphasized the role of Koopman wavefunctions in classical dynamics while their usage in describing hybrid quantum-classical system was presented in [6,43,26,5,20,22].…”