We investigate attractor quantum neural networks (aQNNs) within the framework of coherence theory. We show that: i) aQNNs are associated to non-coherence-generating quantum channels; ii) the depth of the network is given by the decohering power of the corresponding quantum map; and iii) the attractor associated to an arbitrary input state is the one minimizing their relative entropy. Further, we examine faulty aQNNs described by noisy quantum channels, derive their physical implementation and analyze under which conditions their performance can be enhanced by using entanglement or coherence as external resources.

中文翻译：

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相干理论在吸引子量子神经网络中的作用

我们在相干理论的框架内研究吸引子量子神经网络 (aQNN)。我们表明：i）aQNNs 与非相干产生的量子通道相关联；ii) 网络的深度由相应量子图的退相干能力给出；iii) 与任意输入状态相关的吸引子是最小化它们的相对熵的吸引子。此外，我们检查了由噪声量子通道描述的故障 aQNN，推导出它们的物理实现，并分析在哪些条件下可以通过使用纠缠或相干作为外部资源来增强它们的性能。