Entanglement Entropy Production In Quantum Neural Networks

Heruitgegeven door Plato

volgers: 0

Marco Ballarín^1,2,3, Stefano Mangini^1,4,5, Simone Montangero^2,3,6, Chiara Macchiavello^4,5,7en Riccardo Mengoni⁸

¹Deze auteurs hebben in gelijke mate bijgedragen aan dit werk
²Dipartimento di Fisica e Astronomia "G. Galilei", via Marzolo 8, I-35131, Padova, Italy
³INFN, Sezione di Padova, via Marzolo 8, I-35131, Padua, Italië
⁴Dipartimento di Fisica, Università di Pavia, Via Bassi 6, I-27100, Pavia, Italië
⁵INFN Sezione di Pavia, Via Bassi 6, I-27100, Pavia, Italië
⁶Padua Quantum Technologies Research Center, Università degli Studi di Padova
⁷CNR-INO - Largo E. Fermi 6, I-50125, Firenze, Italy
⁸CINECA Quantum Computing Lab,Via Magnanelli, 6/3, 40033 Casalecchio di Reno, Bologna, Italië

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Abstract

Quantum Neural Networks (QNN) worden beschouwd als een kandidaat voor het behalen van kwantumvoordeel in het tijdperk van de Noisy Intermediate Scale Quantum Computer (NISQ). Er zijn verschillende QNN-architecturen voorgesteld en met succes getest op benchmarkdatasets voor machinaal leren. Kwantitatieve onderzoeken naar de door QNN gegenereerde verstrengeling zijn echter slechts voor een beperkt aantal qubits onderzocht. Tensornetwerkmethoden maken het mogelijk kwantumcircuits met een groot aantal qubits in een grote verscheidenheid aan scenario's te emuleren. Hier gebruiken we matrixproducttoestanden om recent bestudeerde QNN-architecturen te karakteriseren met willekeurige parameters tot vijftig qubits, wat aantoont dat hun verstrengeling, gemeten in termen van verstrengelingsentropie tussen qubits, neigt naar die van Haar gedistribueerde willekeurige toestanden naarmate de diepte van de QNN toeneemt. . We certificeren de willekeur van de kwantumtoestanden ook door de expressibiliteit van de circuits te meten, en door tools uit de willekeurige matrixtheorie te gebruiken. We laten een universeel gedrag zien voor de snelheid waarmee verstrengeling wordt gecreëerd in een bepaalde QNN-architectuur, en introduceren daarom een nieuwe maatstaf om de verstrengelingsproductie in QNN's te karakteriseren: de verstrengelingssnelheid. Onze resultaten karakteriseren de verstrengelingseigenschappen van kwantumneurale netwerken en leveren nieuw bewijs van de snelheid waarmee deze willekeurige eenheden benaderen.

Featured image: Graphical representation of QNN and MPS. (a) QNN structure with alternating feature map F and variational ansatz V . Note that the ansatz parameters are different in each layer, while the feature map parameters are the same throughout the whole circuit. (b) MPS diagram. Each sphere is a tensor, representing a qubit qj . The entanglement entropy between bi-partitions A and B is computed by "cutting" the connecting edge ej . (c) Circuits analyzed in the manuscript, depicted with a linear entanglement topology, i.e. entangling gates are only applied between nearest neighbors on a line. (d) Different entanglement topologies: circular, with the first and last qubit of the line connected, and full, where the entangling gates are applied between each pair of qubits.

► BibTeX-gegevens

@article{Ballarin2023entanglemententropy, doi = {10.22331/q-2023-05-31-1023}, url = {https://doi.org/10.22331/q-2023-05-31-1023}, title = {Entanglement entropy production in {Q}uantum {N}eural {N}etworks}, author = {Ballarin, Marco and Mangini, Stefano and Montangero, Simone and Macchiavello, Chiara and Mengoni, Riccardo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1023}, month = may, year = {2023}
}

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Geciteerd door

[1] Yuchen Guo and Shuo Yang, "Noise effects on purity and quantum entanglement in terms of physical implementability", npj Quantum-informatie 9, 11 (2023).

[2] Dirk Heimann, Gunnar Schönhoff, and Frank Kirchner, "Learning capability of parametrized quantum circuits", arXiv: 2209.10345, (2022).

Bovenstaande citaten zijn afkomstig van SAO / NASA ADS (laatst bijgewerkt met succes 2023-06-06 14:08:58). De lijst is mogelijk onvolledig omdat niet alle uitgevers geschikte en volledige citatiegegevens verstrekken.

On Crossref's geciteerde dienst er zijn geen gegevens gevonden over het citeren van werken (laatste poging 2023-06-06 14:08:57).

Dit artikel is gepubliceerd in Quantum onder de Creative Commons Naamsvermelding 4.0 Internationaal (CC BY 4.0) licentie. Het auteursrecht blijft berusten bij de oorspronkelijke houders van auteursrechten, zoals de auteurs of hun instellingen.