scholarly journals The structure of fixed-point tensor network states characterizes the patterns of long-range entanglement

2017 ◽  
Vol 96 (3) ◽  
Author(s):  
Zhu-Xi Luo ◽  
Ethan Lake ◽  
Yong-Shi Wu
Keyword(s):  
Fixed Point ◽  
Long Range ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

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 Plaquette renormalization scheme for tensor network states

2011 ◽  
Vol 83 (5) ◽  
Author(s):  
Ling Wang ◽  
Ying-Jer Kao ◽  
Anders W. Sandvik
Keyword(s):  
Renormalization Scheme ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

scholarly journals Universal photonic quantum computation via time-delayed feedback

2017 ◽  
Vol 114 (43) ◽  
pp. 11362-11367 ◽  
Author(s):  
Hannes Pichler ◽  
Soonwon Choi ◽  
Peter Zoller ◽  
Mikhail D. Lukin
Keyword(s):  
Single Atom ◽  
Many Body ◽  
Cluster States ◽  
Quantum Emitter ◽  
Tensor Network ◽  
Quantum Feedback ◽  
Network States ◽  
Tensor Network States ◽  
Photonic Quantum Computation ◽  
Time Delayed Feedback

We propose and analyze a deterministic protocol to generate two-dimensional photonic cluster states using a single quantum emitter via time-delayed quantum feedback. As a physical implementation, we consider a single atom or atom-like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits, while the mirror allows the implementation of feedback. We identify the class of many-body quantum states that can be produced using this approach and characterize them in terms of 2D tensor network states.

scholarly journals Fermionic Orbital Optimization in Tensor Network States

2016 ◽  
Vol 117 (21) ◽  
Author(s):  
C. Krumnow ◽  
L. Veis ◽  
Ö. Legeza ◽  
J. Eisert
Keyword(s):  
Orbital Optimization ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

scholarly journals Proposal for Quantum Simulation via All-Optically-Generated Tensor Network States

2018 ◽  
Vol 120 (13) ◽  
Author(s):  
I. Dhand ◽  
M. Engelkemeier ◽  
L. Sansoni ◽  
S. Barkhofen ◽  
C. Silberhorn ◽  
...  
Keyword(s):  
Quantum Simulation ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

scholarly journals Concatenated tensor network states

2010 ◽  
Vol 12 (2) ◽  
pp. 025004 ◽  
Author(s):  
R Hübener ◽  
V Nebendahl ◽  
W Dür
Keyword(s):  
Tensor Network ◽  
Network States ◽  
Tensor Network States

Tensor network states and ground-state fidelity for quantum spin ladders

2012 ◽  
Vol 86 (6) ◽  
Author(s):  
Sheng-Hao Li ◽  
Qian-Qian Shi ◽  
Yao-Heng Su ◽  
Jin-Hua Liu ◽  
Yan-Wei Dai ◽  
...  
Keyword(s):  
Ground State ◽  
Quantum Spin ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

scholarly journals Generalized Lanczos method for systematic optimization of tensor network states

2018 ◽  
Vol 27 (7) ◽  
pp. 070501 ◽  
Author(s):  
Rui-Zhen Huang ◽  
Hai-Jun Liao ◽  
Zhi-Yuan Liu ◽  
Hai-Dong Xie ◽  
Zhi-Yuan Xie ◽  
...  
Keyword(s):  
Lanczos Method ◽  
Tensor Network ◽  
Systematic Optimization ◽  
Network States ◽  
Tensor Network States

scholarly journals On the geometry of tensor network states

2012 ◽  
Vol 12 (3&4) ◽  
pp. 346-354
Author(s):  
Joseph M. Landsburg ◽  
Yang Qi ◽  
Ke Ye
Keyword(s):  
Graphical Models ◽  
Matrix Multiplication ◽  
Algebraic Statistics ◽  
Geometric Complexity ◽  
Network State ◽  
Geometric Complexity Theory ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor networks states corresponding to trees and loops. Grasedyck's question has a surprising connection to the area of Geometric Complexity Theory, in that the result is equivalent to the statement that the boundary of the Mulmuley-Sohoni type variety associated to matrix multiplication is strictly larger than the projections of matrix multiplication (and re-expressions of matrix multiplication and its projections after changes of bases). Tensor Network States are also related to graphical models in algebraic statistics.

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