Decoherence in Two-Dimensional Quantum Random Walks with Traps

TL;DR

This paper studies how randomly distributed traps cause decoherence in two-dimensional quantum random walks, affecting the walker's distribution and transition from quantum to classical behavior.

Contribution

It demonstrates the impact of traps as a source of decoherence and reveals non-trivial temporal behavior in the walker's distribution.

Findings

Traps induce significant quantum decoherence.

Quantum to classical transition depends on trap density.

Temporal dependence of standard deviation is non-trivial.

Abstract

Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical transition is examined as a function of the density of the traps. It is shown that traps act as a serious and additional source of quantum decoherence. Furthermore, non-trivial temporal dependence of the standard deviation of the probability distribution of the walker is found when the trapping imperfections are introduced.