Decoherence in Discrete Quantum Walks

We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our results on the effects of decoherence on these quantum walks on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence can be to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms, such as fast mixing times to uniform distributions.Comment: 15 pages, Springer LNP latex style, submitted to Proceedings of DICE 200

Verifying Atom Entanglement Schemes by Testing Bell's Inequality

Recent experiments to test Bell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted and observing a violation of Bell's inequality is the only way to test whether a scheme works with a high precision or not.Comment: Proceedings for the conference Garda 2000, to appear in Zeitschrift fuer Naturforschung, 7 pages, 7 figure

Decoherence can be useful in quantum walks

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.Comment: (Imperial College London) 6 (+epsilon) pages, 6 embedded eps figures, RevTex4. v2 minor changes to correct typos and refs, submitted version. v3 expanded into article format, extra figure, updated refs, Note on "glued trees" adde

Controlling discrete quantum walks: coins and intitial states

In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the possibilities on regular graphs, and also reports periodic behaviour on small cyclic graphs.Comment: 10 (+epsilon) pages, 10 embedded eps figures, typos corrected, references added and updated, corresponds to published version (except figs 5-9 optimised for b&w printing here

Quantum quincunx in cavity quantum electrodynamics

Published versio

Quantum computing in a macroscopic dark period

Published versio