Description
Recent progress in Noisy Intermediate-Scale Quantum (NISQ) devices has motivated increasing interest in their potential application to computationally demanding physics problems [1,2]. In plasma physics, the solution of Partial Differential Equations (PDEs), such as the Helmholtz and Grad–Shafranov equations, is central to the modelling of electromagnetic wave propagation and plasma equilibria. This work assesses the feasibility of applying near-term quantum algorithms to plasma-relevant wave problems, with a focus on electromagnetic eigenvalue formulations.
As a representative benchmark, we calculate the propagation modes of a hollow rectangular waveguide [3,4], with the longer-term objective of extending the approach to plasma-filled configurations. The vacuum waveguide provides a controlled test case that captures essential features of electromagnetic boundary value problems encountered in fusion devices while avoiding additional complexity associated with plasma dielectric models. This makes it a suitable first step towards quantum-based electromagnetic solvers for fusion applications.
We implement a hybrid quantum–classical Variational Quantum Algorithm (VQA) using Qiskit [5], an open-source quantum computing SDK based on Python, in which a parameterized quantum circuit is used to estimate expectation values associated with wave states, while a classical optimizer iteratively updates the circuit parameters to converge towards the physical solution. To maintain sufficient fidelity on current platforms, simulations are limited to a maximum of seven qubits, as increasing circuit size leads to rapidly growing error rates on present-day hardware.
Within this regime, the quantum simulations successfully reproduce classical solutions for fundamental Transverse Electric (TE) and Transverse Magnetic (TM) modes, achieving relative errors in agreement with classical solvers to four decimal places. We observe a near-linear reduction in error with increasing qubit count, while accurate convergence requires a circuit depth at least comparable to the number of qubits, consistent with earlier studies [3].
While simulations on ideal statevector backends demonstrate excellent performance, execution on current-generation quantum hardware is constrained by the large number of measurement shots required within the variational optimization loop. These results indicate that, although VQAs are mathematically capable of solving plasma-relevant electromagnetic wave equations with high precision, their practical application to realistic plasma geometries will require substantial reductions in measurement overhead or advances in next-generation quantum hardware.