Lazy Open Quantum Walks

Abstract

Open quantum walks (OQWs) describe a quantum walker on an underlying graph whose dynamics is purely driven by dissipation and decoherence. Mathematically, they are formulated as completely positive trace preserving (CPTP) maps on the space of density matrices for the walker on the graph. Any microscopically derived OQW must include the possibility of remaining on the same site on the graph when the map is applied. We extend the CPTP map to describe a lazy OQW. We derive a central limit theorem for lazy OQWs on a $d$-dimensional lattice, where the distribution converges to a Gaussian. We show that the properties of this Gaussian computed using conventional methods agree with the general formulas derived from our central limit theorem.

References in corpus (25)

• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• Quantum walks: a comprehensive review
• On the relationship between continuous- and discrete-time quantum walk
• One-Dimensional Three-State Quantum Walk
• Open Quantum Random Walks
• Grover Search with Lackadaisical Quantum Walks
• Open Quantum Walks on Graphs
• A Pathwise Ergodic Theorem for Quantum Trajectories
• Faster Search by Lackadaisical Quantum Walk
• Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
• Limit theorems for open quantum random walks
• Limit distributions of three-state quantum walks: the role of coin eigenstates
• Homogeneous Open Quantum Random Walks on a lattice
• Experimental demonstration of quantum walks with initial superposition states
• The Open Quantum Brownian Motion
• Open quantum random walks: bi-stability on pure states and ballistically induced diffusion
• Lackadaisical quantum walk for spatial search
• Central limit theorem for reducible and irreducible open quantum walks
• Search by Lackadaisical Quantum Walk with Nonhomogeneous Weights
• Microscopic derivation of Open Quantum Walks
• Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory
• Properties of Open Quantum Walks on $\mathbb{Z}$
• One dimensional lazy quantum walks and occupancy rate
• Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks

Cited by in corpus (4)

• On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
• Simulating noisy quantum channels via quantum state preparation algorithms
• Optimal quantum simulation of open quantum systems
• Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs