Quantum Simulation of the Dirac Particle

Abstract

In this paper, we examine whether a quantum computer can efficiently simulate time evolution of the Dirac particle. We consider a Gaussian wave packet scattered by a step potential. We compare the results obtained from a quantum algorithm with the results of classical simulations (Cayley's method) and analytical calculations.

Quantum simulation of the tunnel effect

“…The quantum algorithm simulating the Schrödinger particle has been exhaustively described in our earlier work [7]. Its modification for the case of the particle with spin (Pauli particle) has been successfully examined in [8]. It is based on the Quantum Fourier Transform and the procedure of diagonalisation of a time evolution operator.…”