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International Conference on Electromagnetics in Advanced Applications (ICEAA)

Quantum Information Science and Wave Propagation in Plasmas

Abhay K. Ram, Efstratios Koukoutsis, Kyriakos Hizanidis, George Vahala, Min Soe, Linda L. Vahala

Published Oct 9, 2023• 1 citation
Publisher

Abstract

Quantum computers, through quantum entanglement and parallelization, offer an intriguing prospect of exponential speedup relative to classical computers for performing numerical simulations. Our interest is in the application of quantum information science to plasma physics in order to develop algorithms which can implemented on quantum computers. Concurrently, we want to test these algorithms on present conventional (classical) computers as large scale, error-correcting quantum computers with long coherence times are not yet forthcoming. Even though the constituents of laboratory and space plasmas are electrons and ions, the physics of these plasmas is dominated by collective processes. Quantum effects that are prominent at sub-atomic scales are averaged out in the statistical description of a plasma. Consequently, we need to render classical plasma physics in the language of quantum mechanics in preparation for quantum computers.

DOI
10.1109/iceaa57318.2023.10297667

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Quantum computers, through quantum entanglement and parallelization, offer an intriguing prospect of exponential speedup relative to classical computers for performing numerical simulations. Our interest is in the application of quantum information science to plasma physics in order to develop algorithms which can implemented on quantum computers. Concurrently, we want to test these algorithms on present conventional (classical) computers as large scale, error-correcting quantum computers with long coherence times are not yet forthcoming. Even though the constituents of laboratory and space plasmas are electrons and ions, the physics of these plasmas is dominated by collective processes. Quantum effects that are prominent at sub-atomic scales are averaged out in the statistical description of a plasma. Consequently, we need to render classical plasma physics in the language of quantum mechanics in preparation for quantum computers.
The prospect that quantum computers could be exponentially faster than conventional computers has motivated our research on the application of quantum information science to plasma physics. Quantum computers leverage quantum parallelization, entanglement, and superposition to speed up computations. However, our usual approach to computations on topics in classical plasma physics is not directly suited to take advantage of quantum computers. In this presentation, we will put forth some ideas on formulating algorithms for electromagnetic wave propagation in plasmas which could be implemented on quantum computers.
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.
Electromagnetic waves are an inherent part of all plasmas—laboratory fusion plasmas or astrophysical plasmas. The conventional methods for studying properties of electromagnetic waves rely on discretization of Maxwell equations suitable for implementing on classical, present day, computers. The traditional methodology is not efficient for quantum computing implementation—a future computational source offering a tantalizing possibility of enormous speed up and a significant reduction in computational cost. This paper addresses two topics relevant to implementing Maxwell equations on a quantum computer. The first is on formulating a quantum Schrödinger representation of Maxwell equations for wave propagation in a cold, inhomogeneous, and magnetized plasma. This representation admits unitary, energy preserving, evolution and conveniently lends itself to appropriate discretization for a quantum computer. Riding on the coattails of these results, the second topic is on developing a sequence of unitary operators which form the basis for a qubit lattice algorithm (QLA). The QLA, suitable for quantum computers, can be implemented and tested on existing classical computers for accuracy as well as scaling of computational time with the number of available processors. In order to illustrate the QLA for Maxwell equations, results are presented from a time evolving, full wave simulation of propagation and scattering of an electromagnetic wave packet by non-dispersive dielectric medium localized in space.
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.
Can quantum computers effectively simulate the propagation and scattering of electromagnetic waves in a classical plasma? This chapter introduces some of the basic concepts in mathematics and physics essential to answering that question. The numerical simulations of Maxwell equations for wave propagation in dielectrics are constrained by technological limitations of the present-day computers. In contrast, there has been ample fanfare around quantum computers and their potential to far exceed the performance of traditional computers. Whether the enhanced capabilities of a quantum computer can be put to use for simulating topics in classical physics is a source of intrigue and curiosity.
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.