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Quantum lattice gas representation of some classical solitons. (English) Zbl 1011.35113
Summary: A quantum lattice gas representation is determined for both the non-linear Schrödinger (NLS) and Korteweg-de Vries (KdV) equations. There is excellent agreement with the solutions from these representations to the exact soliton-soliton collisions of the integrable NLS and KdV equations. These algorithms could, in principle, be simulated on a hybrid quantum-classical computer.

35Q51 Soliton equations
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B10 Quantum equilibrium statistical mechanics (general)
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
Full Text: DOI
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