Quantum Signal Processing for simulating radiofrequency waves in plasmas*

Quantum computing is gaining attention as a potential way to speed up simulations of physical systems. The most promising algorithm for general-purpose linear quantum simulations appears to be Quantum Signal Processing (QSP), which has been developed recently and scales optimally with the evolution time and the desired precision [1]. We show how to apply the QSP  to modeling cold linear radiofrequency waves in plasma. The electromagnetic wave field and plasma velocity are encoded into a ``state vector'' that satisfies a multi-dimensional Schrodinger equation with a Hermitian Hamiltonian. We show how to discretize this equation and how to construct a quantum circuit that implements the corresponding Hamiltonian evolution via QSP. The modeling is performed on an emulator of a noiseless quantum computer using a parallelized library QuEST [4]. We also discuss possible applications of the QSP framework to more complex plasma systems.

1. G. H. Low and I. L. Chuang, Quantum 3, 163 (2019).

2. A. Engel, G. Smith, and S. E. Parker, Phys. Rev. A 100, 062315 (2019).

3. I. Y. Dodin and E. A. Startsev, arXiv:2005.14369.

4. T. Jones et al., Sci. Rep. 9, 107736 (2019).