Continuous-Time Quantum Random Walks Require Discrete Space

Abstract

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

19 pages, 9 figures, to appear in J. Phys. A

References in corpus (9)

• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• A Quantum Random Walk Search Algorithm
• Spatial search by quantum walk
• Experimental Implementation of the Quantum Random-Walk Algorithm
• Connecting the discrete and continuous-time quantum walks
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Continuous-time Quantum Walks on a Cycle Graph
• Quantum Random Walks do not need a Coin Toss

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• Dynamics of Rydberg excitations and quantum correlations in an atomic array coupled to a photonic crystal waveguide
• Highly noise resistant multipartite quantum correlations
• Single-point position and transition defects in continuous time quantum walks
• QSW_MPI: a framework for parallel simulation of quantum stochastic walks
• Steepest Entropy Ascent Solution for a Continuous-Time Quantum Walker