Theoretical Studies on Quantum Walks with a Time-varying Coin

Abstract

Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically time-varying coin both numerically and analytically, in order to explore the controllability of quantum walks while preserving its random nature. Quantum walk with a time-varying coinLet us consider a quantum walk with a time-varying coin on a line. In random walks, the walker moves one step to right or left depending on the outcome of the coin toss. A quantum walk is a quantummechanical counterpart of the classical random walk. Then, a quantum walk lives in a bipartite system comprising positions and coin degrees of freedom represented as an entire Hilbert space H = H p ⊗ H c ,