Average position in quantum walks with a U(2) coin

Abstract

We investigated discrete-time quantum walks with an arbitary unitary coin. Here we discover that the average position $<x>=\max (<x>\sin (\alpha +\gamma )$, while the initial state is $1/\sqrt{2}(\mid 0L>+i\mid 0R>)$. We prove the result and get some symmetry properties of quantum walks with a U(2) coin with $\mid 0L>$ and $\mid 0R>$ as the initial state.

References in corpus (3)

• Universal computation by quantum walk
• Spatial search by quantum walk
• Optimizing the discrete time quantum walk using a SU(2) coin

Cited by in corpus (4)

• Generic Quantum Walks with Memory
• Non-Markovian Decoherent Quantum Walks
• Parrondo's paradox for discrete-time quantum walks in momentum space
• Localization and Recurrence of Quantum Walk in Periodic Potential on a Line