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Title: Weaving and neural complexity in symmetric quantum states

Abstract

Here, we study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any order, where the weights are proportional to the correlation order. The neural complexity, originally introduced to characterize correlation patterns in classical neural networks, is here extended to the quantum scenario. We derive closed formulas of the two quantities for GHZ states mixed with white noise.

Authors:
 [1]; ORCiD logo [2]
  1. Univ. de Cordoba, Monteria (Colombia)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1417826
Alternate Identifier(s):
OSTI ID: 1548874
Report Number(s):
LA-UR-17-29411
Journal ID: ISSN 0030-4018
Grant/Contract Number:  
AC52-06NA25396; 20170675PRD2
Resource Type:
Accepted Manuscript
Journal Name:
Optics Communications
Additional Journal Information:
Journal Volume: 413; Journal Issue: C; Journal ID: ISSN 0030-4018
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics; Quantum Correlations, Quantum Many-Body Systems, Complexity

Citation Formats

Susa, Cristian E., and Girolami, Davide. Weaving and neural complexity in symmetric quantum states. United States: N. p., 2017. Web. doi:10.1016/j.optcom.2017.12.050.
Susa, Cristian E., & Girolami, Davide. Weaving and neural complexity in symmetric quantum states. United States. doi:10.1016/j.optcom.2017.12.050.
Susa, Cristian E., and Girolami, Davide. Wed . "Weaving and neural complexity in symmetric quantum states". United States. doi:10.1016/j.optcom.2017.12.050. https://www.osti.gov/servlets/purl/1417826.
@article{osti_1417826,
title = {Weaving and neural complexity in symmetric quantum states},
author = {Susa, Cristian E. and Girolami, Davide},
abstractNote = {Here, we study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any order, where the weights are proportional to the correlation order. The neural complexity, originally introduced to characterize correlation patterns in classical neural networks, is here extended to the quantum scenario. We derive closed formulas of the two quantities for GHZ states mixed with white noise.},
doi = {10.1016/j.optcom.2017.12.050},
journal = {Optics Communications},
number = C,
volume = 413,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
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Figures / Tables:

Figure 1 Figure 1: Correlations of order higher than k, S k→N , and components C(k) of the neural complexity, for N = 5, 7, 10 and 50 qubits. The grey scale goes from black to white as k increases. A zoom of both quantities for the N = 50 case ismore » shown in the insets.« less

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.