The impact of architecture and cost function on dissipative quantum neural networks

Abstract Combining machine learning and quantum computation is a potential path towards powerful applications on quantum devices. Among such approaches, quantum neural networks have emerged as a promising framework. In this work, we present a novel architecture for dissipative quantum neural networks (DQNNs) in which each building block can implement any quantum channel, thus introducing a clear notion of universality suitable for the quantum framework. To this end, we reformulate DQNNs using isometries instead of the conventionally used unitaries, thereby reducing the number of parameters in these models. We furthermore derive a versatile one-to-one parametrization of isometries, facilitating the practical implementation of the proposed structure. Focusing on the impact of different objective functions on the optimization process, we numerically investigate the trainability of extended DQNNs. Our results identify the Hilbert-Schmidt distance as a readily measurable cost function that enables efficient and reliable model optimization. These findings advance both the theoretical understanding and the experimental implementability of quantum neural networks.