The role of data embedding in equivariant quantum convolutional neural networks
Year: 2024
Authors: Das S., Martina S., Caruso F.
Autors Affiliation: Consiglio Nazl Ric CNR INO, Ist Nazl Ott, I-50019 Sesto Fiorentino, Italy; Univ Florence, Dept Phys & Astron, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Univ Florence, European Lab Nonlinear Spect LENS, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy; UIB, CSIC, Inst Cross Disciplinary Phys & Complex Syst IFISC, Campus Univ Illes Balears, Palma De Mallorca 07122, Spain.
Abstract: Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently, this idea has been incorporated into the field of quantum machine learning, which has given rise to equivariant quantum neural networks (EQNNs). In this work, we investigate the role of classical-to-quantum embedding on the performance of equivariant quantum convolutional neural networks (EQCNNs) for the classification of images. We discuss the connection between the data embedding method and the resulting representation of a symmetry group and analyze how changing representation affects the expressibility of an EQCNN. We numerically compare the classification accuracy of EQCNNs with three different basis-permuted amplitude embeddings to the one obtained from a non-equivariant quantum convolutional neural network (QCNN). Our results show a clear dependence of classification accuracy on the underlying embedding, especially for initial training iterations. The improvement in classification accuracy of EQCNN over non-equivariant QCNN may be present or absent depending on the particular embedding and dataset used. The noisy simulation using simple noise models shows that certain EQCNNs are more robust to noise than non-equivariant QCNNs. It is expected that the results of this work can be useful to the community for a better understanding of the importance of data embedding choice in the context of geometric quantum machine learning.
Journal/Review: QUANTUM MACHINE INTELLIGENCE
Volume: 6 (2) Pages from: 82-1 to: 82-15
More Information: S.D. and S.M. thank Paolo Braccia for useful discussions regarding some of the initial ideas. This work was financially supported by the European Union’s Horizon 2020 research and innovation programme under FET-OPEN GA No. 828946-PATHOS and by the European Commission’s Horizon Europe Framework Programme under the Research and Innovation Action GA No.101070546-MUQUABIS. S.M. also acknowledges financial support from the PNRR MUR project PE0000023-NQSTI. F.C. also acknowledges financial support by the European Defence Agency under the project Q-LAMPS Contract No. B PRJ-RT-989 and by the MUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2022- project n. 20227HSE83 (ThAI-MIA) funded by the European Union-Next Generation EU.KeyWords: Machine learning; Quantum neural network; Geometric quantum machine learning; Equivaraint quantum neural networksDOI: 10.1007/s42484-024-00215-7