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.
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.
Its complexity constrains advancements in fusion energy and high energy applications driven by plasma physics, multiscale phenomena beyond classical computing limits. These transformative solutions, especially in plasma simulations, for which exponential speedup is possible, represent significant promise toward breakthroughs in sustainable energy and extreme state studies. In this review, Quantum Computing (QC) is explored as a means to drive plasma physics simulations forward by providing applications such as fusion energy and high-energy systems. This includes computational methods for simulating turbulence, wave-particle interactions, and Magnetohydrodynamic (MHD) instabilities that have near-quantum efficiency. We show that by integrating QC into plasma research, one can solve large-scale linear equations, compute eigenvalues, and optimize complex systems, performing better than classical methods. This discussion examines the potential of quantum computing for plasma physics, highlighting its current limitations, including hardware constraints and the need for specialized algorithms tailored to model complex plasma phenomena accurately. These challenges notwithstanding, QC has the potential to dramatically change plasma modeling and expedite the development of fusion reactors. QC represents a new approach to engineer away computational bottlenecks, providing unprecedented views of plasma behavior needed for sustainable energy breakthroughs. The results from this work underscore the continued importance of looking outside of plasma physics to realize QC’s full potential in advancing high-energy science.
Plasma simulations for magnetic-confinement fusion (MCF) involve high-dimensional kinetic dynamics, strong nonlinear coupling, complex geometries, and multiscale spatiotemporal behavior, imposing severe computational bottlenecks. While quantum computing offers a potential alternative for accelerating plasma simulation problems, its practical advantage for fusion research has not yet been demonstrated. We review existing quantum computing studies across kinetic dynamics, wave interactions, equilibrium, and macroscopic stability, evaluating their hardware implementations and operational bottlenecks. Current studies remain largely restricted to linearized equations, reduced models, or isolated computational subroutines, leaving a substantial gap from realistic fusion simulations. We summarize key problem characteristics, including high dimensionality, structured dynamics, and measurement requirements, under which plasma applications are most likely to yield a quantum advantage. Guided by these considerations, we highlight potential approaches and present a roadmap toward practical quantum advantage of simulating plasma in MCF.
This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron–Frobenius evolution operator, and the Koopman–von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendixes. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave–particle interactions through the simulation of quantum maps and of wave–wave interactions important in nonlinear plasma dynamics.
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a transformative change for many industries. In a recent breakthrough [Liu et al., PNAS 2021], the first efficient quantum algorithm for solving nonlinear differential equations was constructed, based on a single condition R<1, where R characterizes the ratio of nonlinearity to dissipation. This result, however, is limited to the class of purely dissipative systems with negative log-norm, which excludes application to many important problems. In this work, we correct technical issues with this and other prior analysis, and substantially extend the scope of nonlinear dynamical systems that can be efficiently simulated on a quantum computer in a number of ways. Firstly, we extend the existing results from purely dissipative systems to a much broader class of stable systems, and show that every quadratic Lyapunov function for the linearized system corresponds to an independent R-number criterion for the convergence of the Carleman scheme. Secondly, we extend our stable system results to physically relevant settings where conserved polynomial quantities exist. Finally, we provide extensive results for the class of non-resonant systems. With this, we are able to show that efficient quantum algorithms exist for a much wider class of nonlinear systems than previously known, and prove the BQP-completeness of nonlinear oscillator problems of exponential size. In our analysis, we also obtain several results related to the Poincaré-Dulac theorem and diagonalization of the Carleman matrix, which could be of independent interest.
Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future. Here, we propose how to do such modeling for cold plasma waves, in particular, for an X wave propagating in an inhomogeneous one-dimensional plasma. The wave system is represented in the form of a vector Schr\"odinger equation with a Hermitian Hamiltonian. Block encoding is used to represent the Hamiltonian through unitary operations that can be implemented on a quantum computer. To perform the modeling, we apply the so-called quantum signal processing algorithm and construct the corresponding circuit. Quantum simulations with this circuit are emulated on a classical computer, and the results show agreement with traditional classical calculations. We also discuss how our quantum circuit scales with the resolution.
The presence of waves in laboratory and space plasma is due to collective processes which are inherently classical in nature. The linear propagation of electromagnetic waves follows from Maxwell equations in which the constitutive relations are obtained using either a kinetic or a fluid description of the plasma. Even though these descriptions require a large number of charged particles inside a Debye sphere, the interparticle distance is long compared to the de Broglie wavelength of any electron or ion in the plasma. As such, quantum effects are negligible and classical treatments have been successful in providing insight into plasma behavior in fusion, terrestrial, and space plasma. However, this does not preclude the exploitation of quantum computers for simulating classical plasma. It requires us to formulate appropriate theoretical models that appear to be “quantum-like” while maintaining the integrity of the classical description of electromagnetic wave propagation in plasma.