Analysis of Decoherence in Linear and Cyclic Quantum Walks

We theoretically analyze the case of noisy Quantum walks (QWs) by introducing four qubit decoherence models into the coin degree of freedom of linear and cyclic QWs. These models include flipping channels (bit flip, phase flip and bit-phase flip), depolarizing channel, phase damping channel and gene...

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Bibliographic Details
Published in:Optics 2021-12, Vol.2 (4), p.236-250
Main Authors: Jayakody, Mahesh N., Nanayakkara, Asiri, Cohen, Eliahu
Format: Article
Language:English
Subjects:
decoherence
Evolution
Probability
quantum walks
quantum-to-classical transition
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Summary:We theoretically analyze the case of noisy Quantum walks (QWs) by introducing four qubit decoherence models into the coin degree of freedom of linear and cyclic QWs. These models include flipping channels (bit flip, phase flip and bit-phase flip), depolarizing channel, phase damping channel and generalized amplitude damping channel. Explicit expressions for the probability distribution of QWs on a line and on a cyclic path are derived under localized and delocalized initial states. We show that QWs which begin from a delocalized state generate mixture probability distributions, which could give rise to useful algorithmic applications related to data encoding schemes. Specifically, we show how the combination of delocalzed initial states and decoherence can be used for computing the binomial transform of a given set of numbers. However, the sensitivity of QWs to noisy environments may negatively affect various other applications based on QWs.
ISSN:2673-3269
2673-3269
DOI:10.3390/opt2040022