The Impact of Architecture and Cost Function on Dissipative Quantum Neural Networks

TL;DR

This paper introduces a universal architecture for dissipative quantum neural networks using isometries, analyzes the impact of cost functions on training, and enhances understanding and implementation of quantum neural networks.

Contribution

It proposes a novel, universal DQNN architecture reformulated with isometries and provides an efficient parametrization, advancing quantum neural network design and training analysis.

Findings

Different cost functions significantly affect trainability.

The isometry-based architecture reduces parameter count.

The approach improves theoretical understanding and practical implementation.

Abstract

Combining machine learning and quantum computation is a potential path towards powerful applications on quantum devices. Regarding this, quantum neural networks are a prominent approach. 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 conventionally used unitaries, thereby reducing the number of parameters in these models. We furthermore derive a versatile one-to-one parametrization of isometries, allowing for an efficient implementation of the proposed structure. Focusing on the impact of different cost functions on the optimization process, we numerically investigate the trainability of extended DQNNs. This unveils significant training differences among the cost functions considered. Our findings facilitate both the theoretical understanding and the experimental implementability of quantum neural networks.