Generalized exceptional quantum walk search

TL;DR

This paper explores new classes of exceptional configurations in quantum walk search, introduces modified models to improve success probability, and defines generalized exceptional configurations with distinct coherence evolution.

Contribution

It introduces the concept of generalized exceptional configurations, extends the understanding of exceptional configurations, and proposes modified quantum walk models for better search success.

Findings

New classes of exceptional configurations on 2D grids

Modified quantum walk models improve success probability

Generalized exceptional configurations exhibit different coherence evolution

Abstract

We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively and the known diagonal configuration can be regarded as its special case. Meanwhile, we give two modified quantum walk models that can improve the success probability in the exceptional configurations by numerical simulation. Furthermore, we introduce the concept of generalized exceptional configuration and consider search by quantum walk on a cycle with Grover coin. We find that the most natural coin combination model (G,-), where G is a Grover diffusion transformation, is a generalized exceptional configuration when just searching one marked vertex on the cycle. In the end, we find generalized exceptional configuration has a different evolution of quantum coherence from exceptional configuration. These extend largely the range of exceptional configuration of quantum walk search in some sense.