Decoherence in two-dimensional quantum walks with two- and four-state coins

2021 ◽  
Author(s):  
Yu-Guang Yang ◽  
Xi-Xi Wang ◽  
Jian Li ◽  
Dan Li ◽  
Yi-Hua Zhou ◽  
...  
Keyword(s):  
Quantum Correlation ◽  
Quantum Systems ◽  
Quantum Walks ◽  
Two Dimensional ◽  
Link Type ◽  
Experimental Implementation ◽  
Spatial Dimensions

Two-dimensional quantum walks using a two-state coin have simpler experimental implementation than two-dimensional quantum walks using a four-state coin. However, decoherence occurs inevitably during the evolution of quantum walks due to the coupling between the quantum systems and their environment. Thus, it is interesting to investigate the robustness against decoherence for two- and four-state two-dimensional quantum walks. Here, we investigate the effects of the decoherence on two- and four-state two-dimensional quantum walks produced by the broken-link-type noise and compare their robustness against the broken-link-type noise. Specifically, we analyze the quantum correlation between the two spatial dimensions x and y by using measurement-induced disturbance for the two-state quantum walks, i.e. the alternate walk and the Pauli walk, and the four-state quantum walks, i.e. the Grover, Hadamard and Fourier walks, respectively. Our analysis shows that the two-state walks are more robust against the broken-link-type noise than the four-state walks.

Neutron diffraction studies of two-dimensional quantum systems

1987 ◽  
Vol 65 (11) ◽  
pp. 1435-1439 ◽  
Author(s):  
H. J. Lauter ◽  
H. P. Schildberg ◽  
H. Godfrin ◽  
H. Wiechert ◽  
R. Haensel
Keyword(s):  
Neutron Diffraction ◽  
Domain Wall ◽  
Quantum Systems ◽  
Incommensurate Phase ◽  
Two Dimensional

The phases of D2 monolayers on graphite between the commensurate and the incommensurate phase have been investigated by neutron diffraction, revealing new features including domain-wall constructions. For the related systems, 3He and 4He adsorbed on graphite, the structure of the solid first and second layers and the interaction between them have been analyzed.

scholarly journals Quantum sensing of noises in one and two dimensional quantum walks

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Tian Chen ◽  
Xiong Zhang ◽  
Xiangdong Zhang
Keyword(s):  
Quantum Walks ◽  
Two Dimensional ◽  
Quantum Sensing

scholarly journals Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

2018 ◽  
Vol 173 ◽  
pp. 06008 ◽  
Author(s):  
Eugene A. Koval ◽  
Oksana A. Koval
Keyword(s):  
Cross Section ◽  
Short Range ◽  
Strong Dependence ◽  
Dipolar Interaction ◽  
Two Dimensional ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Interaction Radius ◽  
Ultracold Polar Molecules ◽  
Spatial Dimensions

We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

scholarly journals Asymmetries in symmetric quantum walks on two-dimensional networks

2005 ◽  
Vol 72 (4) ◽  
Author(s):  
Oliver Mülken ◽  
Antonio Volta ◽  
Alexander Blumen
Keyword(s):  
Quantum Walks ◽  
Two Dimensional ◽  
Symmetric Quantum

scholarly journals Spatial correlated games

2017 ◽  
Vol 4 (11) ◽  
pp. 171361 ◽  
Author(s):  
Ramón Alonso-Sanz
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Strategy ◽  
Variable Degree ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Nash Equilibrium Strategy ◽  
Link Type

This article studies correlated two-person games constructed from games with independent players as proposed in Iqbal et al. (2016 R. Soc. open sci. 3 , 150477. ( doi:10.1098/rsos.150477 )). The games are played in a collective manner, both in a two-dimensional lattice where the players interact with their neighbours, and with players interacting at random. Four game types are scrutinized in iterated games where the players are allowed to change their strategies, adopting that of their best paid mate neighbour. Particular attention is paid in the study to the effect of a variable degree of correlation on Nash equilibrium strategy pairs.

scholarly journals Irrational Versus Rational Charge and Statistics in Two-Dimensional Quantum Systems

2008 ◽  
Vol 100 (11) ◽  
Author(s):  
Claudio Chamon ◽  
Chang-Yu Hou ◽  
Roman Jackiw ◽  
Christopher Mudry ◽  
So-Young Pi ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Two Dimensional
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