scholarly journals Microscopic derivation of open quantum walks

2015 ◽  
Vol 92 (3) ◽  
Author(s):  
Ilya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Quantum Walks ◽  
Open Quantum ◽  
Microscopic Derivation

scholarly journals Microscopic derivation of open quantum walks

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

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 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 on graphs

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

scholarly journals Microscopic Derivation of Open Quantum Walk on Two-Node Graph

2013 ◽  
Vol 20 (03) ◽  
pp. 1340007 ◽  
Author(s):  
Ilya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Master Equation ◽  
Explicit Form ◽  
Quantum Walk ◽  
Microscopic Model ◽  
Quantum Master Equation ◽  
Level System ◽  
Open Quantum ◽  
Microscopic Derivation ◽  
Quantum Coin

A microscopic derivation of an open quantum walk on a two-node graph is presented. It is shown that for the considered microscopic model of the system–bath interaction the resulting quantum master equation takes the form of a generalised master equation. The explicit form of the “quantum coin” operators is derived. The formalism is demonstrated on the example of a two-level system walking on a two-node graph.

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