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Quantum lattice gas model of Dirac particles in 1+1 dimensions

Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac equation to be cast as a unitary finite-difference equation in a high-energy limit. The split evolution operator (with separate kinetic and interaction terms) is useful for efficient quantum simulation. For pedagogical purposes, here we restrict the treatment to Dirac particle dynamics in 1+1 spacetime dimensions. Independent derivations of the quantum algorithm are presented and the model's validity is tested in several quantum simulations by comparing the numerical results against analytical predictions. Using the relativistic quantum algorithm in the case when mc^2 >> pc, quantum simulations of a nonrelativistic particle in an external scalar square well and parabolic potential is presented.