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arXiv · 2403.11989

Encoding of linear kinetic plasma problems in quantum circuits via data compression

Ivan Novikau·Ilya Y. Dodin·Edward A. Startsev
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Abstract

We propose an algorithm for encoding of linear kinetic plasma problems in quantum circuits. The focus is made on modeling electrostatic linear waves in one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov-Amp\`ere system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation $A\psi = b$ to be solved by using the quantum signal processing algorithm. The latter requires encoding of the matrix $A$ in a quantum circuit as a subblock of a unitary matrix. We propose how to encode $A$ in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

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Ivan Novikau, Ilya Y. Dodin, Edward A. Startsev. 2024-03-18. Encoding of linear kinetic plasma problems in quantum circuits via data compression. https://doi.org/10.1017/s0022377824000795

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