Analysis of Absorbing Times of Quantum Walks

Abstract

Quantum walks are expected to provide useful algorithmic tools for quantum computation. This paper introduces absorbing probability and time of quantum walks and gives both numerical simulation results and theoretical analyses on Hadamard walks on the line and symmetric walks on the hypercube from the viewpoint of absorbing probability and time.

LaTeX2e, 14 pages, 6 figures, 1 table, figures revised, references added, to appear in Physical Review A

References in corpus (5)

• Quantum Computation and Decision Trees
• Exponential algorithmic speedup by quantum walk
• An example of the difference between quantum and classical random walks
• Quantum Random Walks Hit Exponentially Faster
• One-dimensional quantum walks with absorbing boundaries

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• Quantum Walks
• Decoherence in Discrete Quantum Walks
• Experimental realization of a momentum-space quantum walk
• Investigation of Continuous-Time Quantum Walk Via Modules of Bose-Mesner and Terwilliger Algebras
• A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
• Quantum Persistence: A Random Walk Scenario
• Conditional Probability Distributions of Finite Absorbing Quantum Walks
• Quantum walks and their algorithmic applications
• Percolation assisted excitation transport in discrete-time quantum walks
• One-dimensional quantum walks with absorbing boundaries
• Study of Quantum Walk over a Square Lattice
• An HHL-Based Algorithm for Computing Hitting Probabilities of Quantum Random Walks
• Symmetry of distribution for the one-dimensional Hadamard walk
• Limit theorems and absorption problems for quantum random walks in one dimension
• Conditional limit measure of one-dimensional quantum walk with absorbing sink
• Symmetry in quantum walks
• Coherent transport over an explosive percolation lattice
• Experimental measurement of quantum first-passage-time distributions
• Crossover from Diffusive to Ballistic Transport in Periodic Quantum Maps
• Relation between quantum walks with tails and quantum walks with sinks on finite graphs