Qubit state transfer via discrete-time quantum walks

TL;DR

This paper presents a method for perfect qubit state transfer using discrete-time quantum walks, introducing an additional coin operator to achieve high-fidelity transfer over arbitrary distances.

Contribution

The authors introduce a novel scheme with an extra coin operator for perfect qubit state transfer in discrete-time quantum walks, highlighting conditions for perfect transfer.

Findings

Perfect state transfer is achievable with identity or flip coin operators.

Biased and Hadamard coins allow finite-distance perfect transfer.

Quantum walks with perfect transfer are inherently periodic.

Abstract

We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect state transfer are periodic.