Simulating conservative and dissipative waves using quantum signal processing algorithms
ORAL
Abstract
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) methods are the state-of-the-art quantum algorithms for Hamiltonian and matrix inversion computation.
We use the QSP to model the time evolution of cold radio-frequency waves in an inhomogeneous one-dimensional plasma. The considered system, where the wave energy is conserved, is described by a Hermitian Hamiltonian. The results from the emulation of the corresponding quantum circuit demonstrate a good agreement with classical simulations.
However, any process that breaks the energy conservation such as dissipation or outgoing boundary conditions turns the system into a non-Hermitian one. Such systems are more challenging to compute by quantum algorithms. We show how to encode a non-Hermitian stationary wave problem into a quantum circuit and model it by the QSVT algorithm. The potential speedup and the drawbacks of the quantum methods are discussed as well.
We use the QSP to model the time evolution of cold radio-frequency waves in an inhomogeneous one-dimensional plasma. The considered system, where the wave energy is conserved, is described by a Hermitian Hamiltonian. The results from the emulation of the corresponding quantum circuit demonstrate a good agreement with classical simulations.
However, any process that breaks the energy conservation such as dissipation or outgoing boundary conditions turns the system into a non-Hermitian one. Such systems are more challenging to compute by quantum algorithms. We show how to encode a non-Hermitian stationary wave problem into a quantum circuit and model it by the QSVT algorithm. The potential speedup and the drawbacks of the quantum methods are discussed as well.
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Publication: [1] I. Y. Dodin and E. A. Startsev, "On applications of quantum computing to plasma simulations," Physics of Plasmas 28, 092101 (2021).<br>[2] I. Novikau, E. A. Startsev, and I. Y. Dodin, "Quantum Signal Processing for simulating cold plasma waves", Phys. Rev. A 105, 062444 (2022).
Presenters
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Ivan Novikau
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA
Authors
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Ivan Novikau
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA
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Ilya Y Dodin
Princeton Plasma Physics Laboratory, Princeton University, PPPL
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Edward A Startsev
Princeton Plasma Physics Lab., Princeton Plasma Physics Laboratory