Relativistic Connection of Discrete- and Continuous-Time Quantum Walks
Quantum walks have deep connections to quantum search algorithms, quantum cellular automata, quantum chaotic maps, and quantum state transfer. One of the earliest connections, due to Feynman, is to the Dirac equation. The mathematical details of this connection are fully explored here by introducing a general solution for the discrete-time quantum walk in one dimension. In onelimit this maps onto a solution of the Dirac equation, exhibiting relativistic wave packet spreading. In an opposite limit this solution becomes equivalent to the continuous-time quantum walk, maintaining much of its relativistic character throughout. New analytical and numerical results are presented, including entanglement, wave packet spreading, and normal and anomalousZitterbewegung.
Journal of Mathematical Physics
Dirac equation, entanglement, quantum computation, quantum walk
Relativistic Connection of Discrete- and Continuous-Time Quantum Walks, Journal of Mathematical Physics
(Accessed November 28, 2023)