scholarly journals Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law

2009 ◽  
Vol 80 (23) ◽  
Author(s):  
L. Tagliacozzo ◽  
G. Evenbly ◽  
G. Vidal
Keyword(s):  
Quantum Systems ◽  
Two Dimensional ◽  
Tensor Network ◽  
Area Law

scholarly journals Criticality in two-dimensional quantum systems: Tensor network approach

2017 ◽  
Vol 95 (15) ◽  
Author(s):  
Shi-Ju Ran ◽  
Cheng Peng ◽  
Wei Li ◽  
Maciej Lewenstein ◽  
Gang Su
Keyword(s):  
Quantum Systems ◽  
Two Dimensional ◽  
Network Approach ◽  
Tensor Network

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 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 Computable Rényi mutual information: Area laws and correlations

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 541
Author(s):  
Samuel O. Scalet ◽  
Álvaro M. Alhambra ◽  
Georgios Styliaris ◽  
J. Ignacio Cirac
Keyword(s):  
Mutual Information ◽  
Correlation Functions ◽  
Quantum Correlations ◽  
Matrix Product ◽  
Many Body ◽  
Von Neumann ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Area Law

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

scholarly journals Tensor network study of two dimensional lattice $\phi^{4}$ theory

2019 ◽  
Author(s):  
Ryo Sakai ◽  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Yoshifumi Nakamura ◽  
Shinji Takeda ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Network

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.

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