Decoherence on Staggered Quantum Walks

Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking polygons and breaking vertices. The evolution operators subject to these noises are obtained and the equivalence to the coined quantum walk model is presented. Further, we numerically analyze the effect of these decoherence models on the two-dimensional grid of $4$-cliques. We examine how these perturbations affect the quantum walk based search algorithm in this graph and how expanding the tessellations intersection can make it more robust against decoherence.Comment: 17 pages, 14 figure

Deterministic quantum search with adjustable parameters: implementations and applications

Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several schemes to achieve the deterministic version, by using the generalized Grover's iteration $G(\alpha,\beta):=S_r(\beta)\, S_o(\alpha)$ composed of phase oracle $S_o(\alpha)$ and phase rotation $S_r(\beta)$. However, in all the existing schemes the value range of $\alpha$ and $\beta$ is limited; for instance, in the three early schemes $\alpha$ and $\beta$ are determined by the proportion of marked states $M/N$. In this paper, we break through this limitation by presenting a search framework with adjustable parameters, which allows $\alpha$ or $\beta$ to be arbitrarily given. The significance of the framework lies not only in the expansion of mathematical form, but also in its application value, as we present two disparate problems which we are able to solve deterministically using the proposed framework, whereas previous schemes are ineffective.Comment: The title and the abstract have been slightly revise