Numerical validation of the quantum lattice Boltzmann scheme in two and three dimensions.
The multidimensional formulation of the quantum lattice Boltzmann (QLB) scheme is validated against analytical solutions of the time-dependent nonrelativistic Schrödinger equation in two and three spatial dimensions. As a result, we demonstrate the viability of the quantum lattice Boltzmann scheme for the numerical solution of the time-dependent Schrödinger equation in multiple spatial dimensions. In addition, the links between the QLB scheme and sequential splitting methods for partial differential equations are also clarified.
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Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy.
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