2020/12/31 by Alexander Engel, Graeme Smith, Scott E. Parker
Computer Science · Physics and Astronomy · #Discretization #Dynamical systems theory #Embedding #Linear dynamical system #Logarithm #Nonlinear system #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum computer #Quantum system #Spectroscopy and Quantum Chemical Studies #physics.plasm-ph #quant-ph
paper · pdf · doi:10.1063/5.0040313
published as Physics of Plasmas 28, 062305 (2021) · 13 pages
openalex publication_date 2021/06/01 · arxiv created 2021/06/10 · arxiv updated 2021/06/14 · openalex created_date 2021/06/22 · openalex updated_date 2026/08/05
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.