From classical to quantum walks with stochastic resetting on networks

Abstract

Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.

13 pages, 6 figures

References in corpus (48)

• Statistical mechanics of complex networks
• A Quantum Random Walk Search Algorithm
• Universal computation by quantum walk
• Quantum walks: a comprehensive review
• Diffusion with Stochastic Resetting
• Spatial search by quantum walk
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Random walks and diffusion on networks
• Stochastic Resetting and Applications
• Photons Walking the Line: A quantum walk with adjustable coin operations
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Realization of a quantum walk with one and two trapped ions
• Quantum walk of a trapped ion in phase space
• Search via Quantum Walk
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Faster quantum walk algorithm for the two dimensional spatial search
• Quantum walk on the line as an interference phenomenon
• Spatial search by quantum walk is optimal for almost all graphs
• Complex Networks from Classical to Quantum
• Quantum stochastic walks: A generalization of classical random walks and quantum walks
• Quantum Navigation and Ranking in Complex Networks
• Quantum dynamics with stochastic reset
• Classical approach to the graph isomorphism problem using quantum walks
• Random walks on networks with stochastic resetting
• Aging and coarsening in isolated quantum systems after a quench: exact results for the quantum $O(N)$ model with $N\to \infty$
• Spectral properties of simple classical and quantum reset processes
• The Staggered Quantum Walk Model
• Open Quantum Walks on Graphs
• Continuous-time random walks with reset events: Historical background and new perspectives
• Asymptotic dynamics of coined quantum walks on percolation graphs
• Coined quantum walks on percolation graphs
• Staggered Quantum Walks on Graphs
• Centrality measure based on continuous-time quantum walks and experimental realization
• Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
• Degree Distribution in Quantum Walks on Complex Networks
• Quantum percolation and transition point of a directed discrete-time quantum walk
• Quantum walk coherences on a dynamical percolation graph
• In and out of equilibrium quantum metrology with mean-field quantum criticality
• Tuning quantum measurements to control chaos
• The Great Divide: Drivers of Polarization in the US Public
• Lindblad dynamics of a quantum spherical spin
• Lindblad dynamics of the quantum spherical model
• Decoherence enhances performance of quantum walks applied to graph isomorphism testing
• Competing Activists--Political Polarization
• Quantum aging and dynamical universality in the long-range $O(N\to \infty )$ model
• Dynamical chaotic phases and constrained quantum dynamics
• Study of Quantum Walk over a Square Lattice
• Random Walks on Complex Networks

Cited by in corpus (17)

• Diffusive transport on networks with stochastic resetting to multiple nodes
• Diffusion processes with Gamma-distributed resetting and non-instantaneous returns
• Random walks on complex networks with first-passage resetting
• Random walks on complex networks under node-dependent stochastic resetting
• Random walks on complex networks under time-dependent stochastic resetting
• Classical and quantum random-walk centrality measures in multilayer networks
• Random walks on complex networks with multiple resetting nodes: a renewal approach
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems
• First passage in discrete-time absorbing Markov chains under stochastic resetting
• Coined quantum walks on the line: Disorder, entanglement, and localization
• Mean first-encounter times of simultaneous random walkers with resetting on networks
• Classical and Quantum Random Walks to Identify Leaders in Criminal Networks
• Recurrence in discrete-time quantum stochastic walks
• Clustering-induced localization of quantum walks on networks
• On the initial value of PageRank