Accelerated first detection in discrete-time quantum walks using sharp restarts

TL;DR

This paper demonstrates that restarting monitored discrete-time quantum walks significantly accelerates target detection, surpassing classical and continuous-time quantum walks by leveraging quantum ballistic propagation and the coin degree of freedom.

Contribution

It shows that restart strategies in discrete-time quantum walks improve search efficiency, outperforming classical and continuous-time quantum walks, and can be optimized using target information.

Findings

Restarted DTQWs outperform classical random walks in target searches.

DTQWs can surpass CTQWs in detection speed without losing quantum advantages.

Knowledge of target parity or position further accelerates search times.

Abstract

Restart is a common strategy observed in nature that accelerates first-passage processes and has been extensively studied using classical random walks. In the quantum regime, restart in continuous-time quantum walks (CTQWs) has been shown to expedite the quantum hitting times. Here, we study how restarting monitored discrete-time quantum walks (DTQWs) affects the quantum hitting times. We show that the restarted DTQWs outperform classical random walks in target searches, benefiting from quantum ballistic propagation, a feature shared with their continuous-time counterparts. Moreover, the explicit coin degree of freedom in DTQWs allows them to surpass even CTQWs in target detection without sacrificing any quantum advantage. Additionally, knowledge of the target's parity or position relative to the origin can be leveraged to tailor DTQWs for even faster searches. Our study paves the way for more efficient use of DTQWs in quantum-walk-based search algorithms, simulations and modeling of quantum transport towards targeted sites in complex quantum networks.