论文标题
纠缠诱发贫瘠的高原
Entanglement Induced Barren Plateaus
论文作者
论文摘要
我们认为，量子神经网络中可见单位和隐藏单元之间的纠缠过多会阻碍学习。特别是，我们表明，满足纠缠熵的体积法的量子神经网络将导致不适合以高概率学习的模型。然后，使用量子热力学的参数，我们表明该体积定律是典型的，并且由于纠缠而引起的优化景观中存在贫瘠的高原。更确切地说，我们表明，对于可见层上的任何有界的目标函数，该目标函数的期望值的Lipshitz常数将以高概率与隐藏系统的维度成反比。我们展示了如何导致梯度下降和无梯度方法失败。我们注意到，量子Boltzmann机器可能会出现类似的问题，尽管需要对隐藏/可见子空间之间的耦合进行更强的假设。我们强调了预处理这种生成模型如何提供一种方法来浏览这些贫瘠的高原。
We argue that an excess in entanglement between the visible and hidden units in a Quantum Neural Network can hinder learning. In particular, we show that quantum neural networks that satisfy a volume-law in the entanglement entropy will give rise to models not suitable for learning with high probability. Using arguments from quantum thermodynamics, we then show that this volume law is typical and that there exists a barren plateau in the optimization landscape due to entanglement. More precisely, we show that for any bounded objective function on the visible layers, the Lipshitz constants of the expectation value of that objective function will scale inversely with the dimension of the hidden-subsystem with high probability. We show how this can cause both gradient descent and gradient-free methods to fail. We note that similar problems can happen with quantum Boltzmann machines, although stronger assumptions on the coupling between the hidden/visible subspaces are necessary. We highlight how pretraining such generative models may provide a way to navigate these barren plateaus.
