scholarly journals Open quantum walks on graphs

2012 ◽  
Vol 376 (18) ◽  
pp. 1545-1548 ◽  
Author(s):  
S. Attal ◽  
F. Petruccione ◽  
I. Sinayskiy
Keyword(s):  
Quantum Walks ◽  
Open Quantum

Higher-dimensional open quantum walk in environment of quantum Bernoulli noises

2021 ◽  
pp. 2250001
Author(s):  
Ce Wang
Keyword(s):  
Quantum Walk ◽  
Quantum Walks ◽  
Initial State ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Higher Dimensional ◽  
Gauss Type ◽  
Open Quantum Random Walks ◽  
Limit Probability ◽  
Creation Operators

Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.

scholarly journals Microscopic derivation of open quantum walks

2014 ◽  
Author(s):  
Ilya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Quantum Walks ◽  
Open Quantum ◽  
Microscopic Derivation

scholarly journals Generalized Open Quantum Walks on Apollonian Networks

PLoS ONE ◽  
2015 ◽  
Vol 10 (7) ◽  
pp. e0130967 ◽  
Author(s):  
Łukasz Pawela ◽  
Piotr Gawron ◽  
Jarosław Adam Miszczak ◽  
Przemysław Sadowski
Keyword(s):  
Quantum Walks ◽  
Open Quantum

scholarly journals Properties of open quantum walks on $\mathbb {Z}$

2012 ◽  
Vol T151 ◽  
pp. 014077 ◽  
Author(s):  
Ilya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Quantum Walks ◽  
Open Quantum

scholarly journals Phase transition of an open quantum walk

2021 ◽  
Author(s):  
Takuya Machida
Keyword(s):  
Phase Transition ◽  
Standard Deviation ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Gaussian Distributions ◽  
Limit Distributions ◽  
Open Quantum

It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate an open quantum walk on [Formula: see text] with parameterized operations in this paper, and study its 1st and 2nd moments so that we find its standard deviation. The standard deviation tells us whether the open quantum walker shows diffusive or ballistic behavior, which results in a phase transition of the walker.

scholarly journals Open Quantum Walks: a short introduction

2013 ◽  
Vol 442 ◽  
pp. 012003 ◽  
Author(s):  
Ilya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Quantum Walks ◽  
Short Introduction ◽  
Open Quantum

scholarly journals A Generalized Quantum Optical Scheme for Implementing Open Quantum Walks

2020 ◽  
Vol 315 ◽  
pp. 83-92
Author(s):  
Ayanda Romanis Zungu ◽  
IIya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Quantum Walks ◽  
Optical Scheme ◽  
Open Quantum ◽  
Quantum Optical

scholarly journals Homogeneous open quantum walks on the line: criteria for site recurrence and absorption

2021 ◽  
Vol 21 (1&2) ◽  
pp. 0037-0058
Author(s):  
Thomas S. Jacq ◽  
Carlos F. Lardizabal
Keyword(s):  
Random Walks ◽  
Nearest Neighbor ◽  
Trace Class ◽  
Quantum Walks ◽  
Internal Degree ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Infinite Line ◽  
Trace Class Operators ◽  
Internal Degree Of Freedom

In this work, we study open quantum random walks, as described by S. Attal et al.. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the recurrence problem for classical, discrete-time random walks. This work focuses on obtaining criteria for site recurrence of nearest-neighbor, homogeneous walks on the integer line, with the description presented here making use of recent results of the theory of open walks, most particularly regarding reducibility properties of the operators involved. This allows us to obtain a complete criterion for site recurrence in the case for which the internal degree of freedom of each site (coin space) is of dimension 2. We also present the analogous result for irreducible walks with an internal degree of arbitrary finite dimension and the absorption problem for walks on the semi-infinite line.

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