"Faster search of clustered marked states with lackadaisical quantum wa" by Amit Saha, Ritajit Majumdar et al.
 

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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