Faster search of clustered marked states with lackadaisical quantum walks

Article Type

Research Article

Publication Title

Quantum Information Processing

Abstract

The nature of discrete-time quantum walks in the presence of multiple marked states can be found in the literature. An exceptional configuration of clustered marked states, which is a variant of multiple marked states, may be defined as a cluster of k marked states arranged in a k×k array within a N×N grid, where k= n2 and n an odd integer. In this article, we establish through numerical simulation that for lackadaisical quantum walks, which is the analogue of a three-state discrete-time quantum walks on a line, the success probability to find a vertex in the marked region of this exceptional configuration is nearly 1 with smaller run-time. We also show that the weights of the self-loop suggested for multiple marked states in the state-of-the-art works are not optimal for this exceptional configuration of clustered marked states. We propose a weight of the self-loop which gives the desired result for this configuration.

DOI

10.1007/s11128-022-03606-6

Publication Date

8-1-2022

Comments

Open Access, Green

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