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A quantum algorithm that solves the time-dependent Dirac equation on adigital quantum computer is developed and analyzed. The time evolution isperformed by an operator splitting decomposition technique that allows for amapping of the Dirac operator to a quantum walk supplemented by unitaryrotation steps in spinor space. Every step of the splitting method isdecomposed into sets of quantum gates. It is demonstrated that the algorithmhas an exponential speedup over the implementation of the same numerical schemeon a classical computer, as long as certain conditions are satisfied. Finally,an explicit decomposition of this algorithm into elementary gates from auniversal set is carried out to determine the resource requirements. It isshown that a proof-of-principle calculation may be possible with actual quantumtechnologies.

Algorithm for the solution of the Dirac equation on digital quantum computers