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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.

MSC:
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)
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