Permutation-equivariant quantum convolutional neural networks
Anno: 2025
Autori: Das S., Caruso F.
Affiliazione autori: CNR, Ist Nazl Ott INO, I-50019 Sesto Fiorentino, Italy; Univ Florence, Dept Phys & Astron, Ital, Via Sansone 1, I-50019 Sesto Fiorentino, Italy; Univ Florence, European Lab Nonlinear Spect LENS, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.
Abstract: The Symmetric group S-n manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. Subgroups of S-n arise, among many other contexts, to describe label symmetry of classical images with respect to spatial transformations, such as reflection or rotation. Equipped with the formalism of geometric quantum machine learning, in this study we propose the architectures of equivariant quantum convolutional neural networks (EQCNNs) adherent to S-n and its subgroups. We demonstrate that a careful choice of pixel-to-qubit embedding order can facilitate easy construction of EQCNNs for small subgroups of S-n. Our novel EQCNN architecture corresponding to the full permutation group S-n is built by applying all possible QCNNs with equal probability, which can also be conceptualized as a dropout strategy in quantum neural networks. For subgroups of S-n, our numerical results using MNIST datasets show better classification accuracy than non-equivariant QCNNs. The S-n-equivariant QCNN architecture shows significantly improved training and test performance than non-equivariant QCNN for classification of connected and non-connected graphs. When trained with sufficiently large number of data, the S-n-equivariant QCNN shows better average performance compared to S-n-equivariant QNN . These results contribute towards building powerful quantum machine learning architectures in permutation-symmetric systems.
Giornale/Rivista: QUANTUM SCIENCE AND TECHNOLOGY
Volume: 10 (1) Da Pagina: 15030-1 A: 15030-14
Maggiori informazioni: This work was supported by the European Commission’s Horizon Europe Framework Programme under the Research and Innovation Action GA No. 101070546-MUQUABIS, by the European Union’s Horizon 2020 research and innovation programme under FET-OPEN GA No. 828946-PATHOS, 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 No. 20227HSE83 – ThAI-MIA funded by the European Union-Next Generation EU.Parole chiavi: quantum machine learning; variational quantum circuit; equivariant quantum neural networkDOI: 10.1088/2058-9565/ad8e80Citazioni: 1dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2025-05-18Riferimenti tratti da Isi Web of Knowledge: (solo abbonati)
