RANDOMIZED METHOD FOR ESTIMATING THE VON NEUMANN ENTROPY OF LARGE-SCALE DENSITY MATRICES

2018 ◽  
Author(s):  
Hayoung Choi ◽  
Xuming Song ◽  
Yuanming Shi
Keyword(s):  
Large Scale ◽  
Von Neumann Entropy ◽  
Density Matrices ◽  
Von Neumann ◽  
Randomized Method

scholarly journals Randomized Linear Algebra Approaches to Estimate the von Neumann Entropy of Density Matrices

2020 ◽  
Vol 66 (8) ◽  
pp. 5003-5021
Author(s):  
Eugenia-Maria Kontopoulou ◽  
Gregory-Paul Dexter ◽  
Wojciech Szpankowski ◽  
Ananth Grama ◽  
Petros Drineas
Keyword(s):  
Linear Algebra ◽  
Von Neumann Entropy ◽  
Density Matrices ◽  
Von Neumann

scholarly journals Symmetric Laplacians, quantum density matrices and their Von-Neumann entropy

2017 ◽  
Vol 532 ◽  
pp. 534-549 ◽  
Author(s):  
David E. Simmons ◽  
Justin P. Coon ◽  
Animesh Datta
Keyword(s):  
Von Neumann Entropy ◽  
Density Matrices ◽  
Von Neumann

scholarly journals Electronic Properties of Carbon Nanobelts Predicted by Thermally-Assisted-Occupation DFT

Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2224
Author(s):  
Sonai Seenithurai ◽  
Jeng-Da Chai
Keyword(s):  
Electronic Properties ◽  
Density Functional ◽  
Large Scale ◽  
Von Neumann Entropy ◽  
Electronic Systems ◽  
Functional Theory ◽  
Von Neumann ◽  
Hartree Fock ◽  
Prediction Of Properties ◽  
Occupation Numbers

Accurate prediction of properties of large-scale multi-reference (MR) electronic systems remains difficult for traditional computational methods (e.g., the Hartree–Fock theory and Kohn–Sham density functional theory (DFT)). Recently, thermally-assisted-occupation (TAO)-DFT has been demonstrated to offer reliable description of electronic properties of various large-scale MR electronic systems. Consequently, in this work, TAO-DFT is used to unlock the electronic properties associated with C-Belt[n] (i.e., the carbon nanobelts containing n fused 12-membered carbon rings). Our calculations show that for all the system sizes reported (n = 4–24), C-Belt[n] have singlet ground states. In general, the larger the size of C-Belt[n], the more pronounced the MR character of ground-state C-Belt[n], as evident from the symmetrized von Neumann entropy and the occupation numbers of active TAO-orbitals. Furthermore, the active TAO-orbitals are delocalized along the circumference of C-Belt[n], as evident from the visualization of active TAO-orbitals.

Maps on Quantum States in -algebras Preserving von Neumann Entropy or Schatten -norm of Convex Combinations

2019 ◽  
Vol 62 (1) ◽  
pp. 75-80 ◽  
Author(s):  
Marcell Gaál
Keyword(s):  
Convex Combination ◽  
General Setting ◽  
Positive Semidefinite ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Density Matrices ◽  
Positive Semidefinite Matrices ◽  
Von Neumann ◽  
Convex Functionals ◽  
Invertible Elements

AbstractVery recently, Karder and Petek completely described maps on density matrices (positive semidefinite matrices with unit trace) preserving certain entropy-like convex functionals of any convex combination. As a result, maps could be characterized that preserve von Neumann entropy or Schatten $p$-norm of any convex combination of quantum states (whose mathematical representatives are the density matrices). In this note we consider these latter two problems on the set of invertible density operators, in a much more general setting, on the set of positive invertible elements with unit trace in a $C^{\ast }$-algebra.

scholarly journals SOME ENTANGLEMENT FEATURES OF HIGHLY ENTANGLED MULTIQUBIT STATES

2008 ◽  
Vol 06 (supp01) ◽  
pp. 605-611 ◽  
Author(s):  
A. BORRAS ◽  
M. CASAS ◽  
A. R. PLASTINO ◽  
A. PLASTINO
Keyword(s):  
Linear Entropy ◽  
Von Neumann Entropy ◽  
Entangled States ◽  
Marginal Density ◽  
Density Matrices ◽  
Von Neumann ◽  
Entanglement Measures

We explore some basic entanglement features of multiqubit systems that are relevant for the development of algorithms for searching highly entangled states. In particular, we compare the behaviours of multiqubit entanglement measures based (i) on the von Neumann entropy of marginal density matrices and (ii) on the linear entropy of those matrices.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

scholarly journals Towards Neuromorphic Learning Machines Using Emerging Memory Devices with Brain-Like Energy Efficiency

2018 ◽  
Vol 8 (4) ◽  
pp. 34 ◽  
Author(s):  
Vishal Saxena ◽  
Xinyu Wu ◽  
Ira Srivastava ◽  
Kehan Zhu
Keyword(s):  
Machine Learning ◽  
Energy Efficiency ◽  
Deep Learning ◽  
Large Scale ◽  
Learning Algorithms ◽  
Memory Devices ◽  
Cognitive Computing ◽  
Mixed Signal ◽  
Von Neumann ◽  
Emerging Memory

The ongoing revolution in Deep Learning is redefining the nature of computing that is driven by the increasing amount of pattern classification and cognitive tasks. Specialized digital hardware for deep learning still holds its predominance due to the flexibility offered by the software implementation and maturity of algorithms. However, it is being increasingly desired that cognitive computing occurs at the edge, i.e., on hand-held devices that are energy constrained, which is energy prohibitive when employing digital von Neumann architectures. Recent explorations in digital neuromorphic hardware have shown promise, but offer low neurosynaptic density needed for scaling to applications such as intelligent cognitive assistants (ICA). Large-scale integration of nanoscale emerging memory devices with Complementary Metal Oxide Semiconductor (CMOS) mixed-signal integrated circuits can herald a new generation of Neuromorphic computers that will transcend the von Neumann bottleneck for cognitive computing tasks. Such hybrid Neuromorphic System-on-a-chip (NeuSoC) architectures promise machine learning capability at chip-scale form factor, and several orders of magnitude improvement in energy efficiency. Practical demonstration of such architectures has been limited as performance of emerging memory devices falls short of the expected behavior from the idealized memristor-based analog synapses, or weights, and novel machine learning algorithms are needed to take advantage of the device behavior. In this article, we review the challenges involved and present a pathway to realize large-scale mixed-signal NeuSoCs, from device arrays and circuits to spike-based deep learning algorithms with ‘brain-like’ energy-efficiency.

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