A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits.
Journal
Nature communications
ISSN: 2041-1723
Titre abrégé: Nat Commun
Pays: England
ID NLM: 101528555
Informations de publication
Date de publication:
22 Aug 2024
22 Aug 2024
Historique:
received:
11
10
2023
accepted:
25
06
2024
medline:
23
8
2024
pubmed:
23
8
2024
entrez:
22
8
2024
Statut:
epublish
Résumé
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit's generators.
Identifiants
pubmed: 39174526
doi: 10.1038/s41467-024-49909-3
pii: 10.1038/s41467-024-49909-3
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
7172Informations de copyright
© 2024. The Author(s).
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