# 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:

- Univ. de Cordoba, Monteria (Colombia)
- 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

- Report Number(s):
- LA-UR-17-29411

Journal ID: ISSN 0030-4018

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: 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.
```

```
@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 = {Wed Dec 27 00:00:00 EST 2017},

month = {Wed Dec 27 00:00:00 EST 2017}

}

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