Negational symmetry of quantum neural networks for binary pattern classification. (September 2022) - Dong, Nanqing; Kampffmeyer, Michael; Voiculescu, Irina; Xing, Eric
Highlights: Formalize, prove, and analyze the negational symmetry of QNNs with full entanglement in binary pattern classification. Propose a representation learning framework for QNNs and generalize the negational symmetry to it. Show that the negational symmetry of QNNs could be a double-edged sword in potential applications. Abstract: Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, the behavior of QNNs in binary pattern classification is still underexplored. In this work, we find that QNNs have an Achilles' heel in binary pattern classification. To illustrate this point, we provide a theoretical insight into the properties of QNNs by presenting and analyzing a new form of symmetry embedded in a family of QNNs with full entanglement, which we term negational symmetry . Due to negational symmetry, QNNs can not differentiate between a quantum binary signal and its negational counterpart. We empirically evaluate the negational symmetry of QNNs in binary pattern classification tasks using Google's quantum computing framework. Both theoretical and experimental results suggest that negational symmetry is a fundamental property of QNNs, which is not shared by classical models. Our findings also imply that negational symmetry is a double-edged sword in practical quantum applications.