Analysis of Decoherence in Linear and Cyclic Quantum Walks

Optics

Asiri Nanayakkara¹  Mahesh N. Jayakody²  Eliahu Cohen² 

[1] National Institute of Fundamental Studies, Kandy 20000, Sri Lanka;The Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 52900, Israel;

关键词: quantum walks;    decoherence;    quantum-to-classical transition;   

DOI  :  10.3390/opt2040022

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown