Entanglement Entropy Production In Quantum Neural Networks

Republicat de Platon

Urmaritori: 0

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

¹Acești autori au contribuit în mod egal la această lucrare
²Dipartimento di Fisica e Astronomia "G. Galilei", via Marzolo 8, I-35131, Padova, Italy
³INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova, Italia
⁴Dipartimento di Fisica, Università di Pavia, Via Bassi 6, I-27100, Pavia, Italia
⁵INFN Sezione di Pavia, Via Bassi 6, I-27100, Pavia, Italia
⁶Padova 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, Italia

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Abstract

Rețelele neuronale cuantice (QNN) sunt considerate un candidat pentru obținerea unui avantaj cuantic în era computerului cuantic la scară intermediară zgomotoasă (NISQ). Mai multe arhitecturi QNN au fost propuse și testate cu succes pe seturi de date de referință pentru învățarea automată. Cu toate acestea, studiile cantitative ale încurcăturii generate de QNN au fost investigate doar pentru până la câțiva qubiți. Metodele de rețea tensorială permit emularea circuitelor cuantice cu un număr mare de qubiți într-o mare varietate de scenarii. Aici, folosim stări de produs matrice pentru a caracteriza arhitecturile QNN studiate recent cu parametri aleatori de până la cincizeci de qubiți, arătând că încrucișarea lor, măsurată în termeni de entropie de încrucișare între qubiți, tinde spre cea a stărilor aleatoare distribuite Haar pe măsură ce adâncimea QNN este crescută. . Certificăm aleatorietatea stărilor cuantice și prin măsurarea expresibilității circuitelor, precum și folosind instrumente din teoria matricelor aleatoare. Arătăm un comportament universal pentru rata la care se creează întanglementul în orice arhitectură QNN dată și, în consecință, introducem o nouă măsură pentru a caracteriza producția de întanglement în QNN-uri: viteza de încurcare. Rezultatele noastre caracterizează proprietățile de întricare ale rețelelor neuronale cuantice și oferă noi dovezi ale ratei la care aceste unități aleatoare aproximative.

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.

► Date BibTeX

@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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Citat de

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