Numerical Methods for Plasma Astrophysics:
From Particle Kinetics to MHD

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Quantum Lattice Representation of 1D MHD

Dr. George Vahala

Physics at College of William and Mary

Abstract:   Quantum lattice algorithms have the potential to solve problems that are insoluble on classical computers due to exponential speed-up achieved by exploiting local quantum entanglement. Here we present some quantum lattice algorithms for the solution of 1D MHD, the nonlinear Schrodinger and KdV equations. The (1D) spatial domain is discretized and 2 qubits/scalar field are required at each spatial node. With an appropriate sequence of unitary collision operators that couple on-site qubits and unitary streaming operators that spread the post-collision state to neighboring spatial nodes, one can recover the desired macroscopic nonlinear equations in the continuum limit. The quantum lattice solutions are compared to the exact soliton solutions with very good agreement.