Theoretical guarantees for permutation-equivariant quantum neural networks

Schatzki, Louis; Larocca, Martín; Nguyen, Quynh T.; Sauvage, Frédéric Antoine; Cerezo de la Roca, Marco Vinicio Sebastian

doi:10.1038/s41534-024-00804-1

Theoretical guarantees for permutation-equivariant quantum neural networks

Journal Article · Sun Jan 21 23:00:00 EST 2024 · npj Quantum Information

DOI:https://doi.org/10.1038/s41534-024-00804-1· OSTI ID:2367485

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Harvard Univ., Cambridge, MA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group $$S_n$$), and show how to build $$S_n$$-equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2367485

Report Number(s):: LA-UR--22-29899

Journal Information:: npj Quantum Information, Journal Name: npj Quantum Information Journal Issue: 1 Vol. 10; ISSN 2056-6387

Publisher:: Nature Partner JournalsCopyright Statement

Country of Publication:: United States

Language:: English

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