# gst: accelerated first detection in discrete-time quantum walks using sharp restarts.

<< 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 [Phys. Rev. Lett. 130, 050802 (2023)]. >>

 Here, AA << study how restarting monitored discrete-time quantum walks (DTQWs) affects the quantum hitting times. (They) 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. >>

Kunal Shukla, Riddhi Chatterjee, C. M. Chandrashekar. Accelerated first detection in discrete-time quantum walks using sharp restarts. Phys. Rev. Research 7, 023069. Apr 21, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023069

Also: walk, random, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, randomness, walk, random walk, quantum walk, stochasticity, sharp restart.

# gst: biased random walks on networks with stochastic resetting.

<< This study explores biased random walk dynamics with stochastic resetting on general networks. (AA) show that the combination of biased random walks and stochastic resetting makes significant contributions by analyzing the search efficiency. (They) derive two analytical expressions for the stationary distribution and the mean first passage time, which are related to the spectral representation of the probability transition matrix of a biased random walk without resetting. These expressions can be used to determine the capacity of a random walker to reach the specific target and probe a finite network. >>

AA << apply the analytical results to two types of networks, pseudofractal scale-free webs and T-fractals, which are constructed through an iterative process. (They) also extend a strategy to explore other complex structure networks or larger networks by leveraging the spectral properties. >>

Anlin Li, Xiaohan Sun. Biased random walks on networks with stochastic resetting. Phys. Rev. E 111, 054309. May 16, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.054309

Also: walk, random, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, randomness, random walk, stochasticity, stochastic resetting.

gst: actually and counterintuitively a coherent jump could generate disorder.

AA << consider a quantized version of a model for “random walk in random environment.” (..) For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. >>

Ben Avnit, Doron Cohen. Quantum walk in stochastic environment. Phys. Rev. E 108, 054111. Nov 7, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054111

Also:  Voli a casaccio. Notes (quasi-stochastic poetry). Oct 01, 2006.

https://inkpi.blogspot.com/2006/10/2066-voli-casaccio.html

Also: 'random', 'transition', 'disorder', 'chaos', in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, random walk, quantum walk, qu-walk, jump, transition, disorder, chaos