标题： 架构和代价函数对耗散量子神经网络的影响 显示英文标题

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

摘要： 将机器学习与量子计算相结合是通往量子设备强大应用的潜在路径。 关于这一点，量子神经网络是一种突出的方法。 在本工作中，我们提出了一种耗散量子神经网络（DQNNs）的新架构，其中每个构建块可以实现任何量子通道，从而引入了一个适合量子框架的清晰的通用性概念。 为此，我们使用等距变换代替通常使用的酉变换来重新表述DQNNs，从而减少了这些模型中的参数数量。 此外，我们推导出一种通用的一对一等距变换参数化方法，使得所提出的结构能够高效实现。 专注于不同代价函数对优化过程的影响，我们数值研究了扩展DQNNs的可训练性。 这揭示了所考虑的代价函数之间的显著训练差异。 我们的发现有助于量子神经网络的理论理解和实验实现。 显示英文摘要

摘要： 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.