By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum walker, initially localized on a lattice, is directly analogous to relativistic wave-packet spreading. Analytic wave-packet solutions reveal a striking connection between the discrete and continuous time quantum walks.
Physical Review Letters
Dirac equation, entanglement, quantum computation, quantum walk
Relativistic Quantum Walks, Physical Review Letters
(Accessed November 28, 2023)