Negational Symmetry of Quantum Neural Networks for Binary Pattern Classification

Entanglement is a physical phenomenon, which has fueled recent successes of quantum algorithms. Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, for the time being, the effect of entanglement in QNNs and the behavior of QNNs in binary pattern classification are still underexplored. In this work, we provide some theoretical insight into the properties of QNNs by presenting and analyzing a new form of invariance embedded in QNNs for both quantum binary classification and quantum representation learning, which we term negational symmetry. Given a quantum binary signal and its negational counterpart where a bitwise NOT operation is applied to each quantum bit of the binary signal, a QNN outputs the same logits. That is to say, QNNs cannot differentiate a quantum binary signal and its negational counterpart in a binary classification task. We further empirically evaluate the negational symmetry of QNNs in binary pattern classification tasks using Google's quantum computing framework. The 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.