论文标题
表征变异量子电路的损失格局
Characterizing the loss landscape of variational quantum circuits
论文作者
论文摘要
机器学习技术通过嘈杂的中间量子量子（NISQ）设备，尤其是变化量子电路（VQC）增强，最近引起了很多兴趣，并且已经针对某些问题进行了基准测试。受经典深度学习的启发，VQC是通过梯度下降方法训练的，这些方法可以在大参数空间上进行有效的训练。对于NISQ大小的电路，此类方法显示出良好的收敛性。但是，仍然有许多与损失函数的收敛性以及在消失梯度的情况下的训练性有关的问题。此外，目前尚不清楚最小值在概括和稳定性方面对数据的扰动是多么“好”，因此，有必要对工具进行定量研究VQC的收敛性。在这项工作中，我们介绍了一种计算VQCS损失函数的Hessian的方法，并展示如何用它来表征损失格局。 Hessian的特征值提供了有关局部曲率的信息，我们讨论了如何将这些信息解释并与经典的神经网络进行比较。我们以几个示例进行了基准测试，从一个简单的分析玩具模型开始，以提供有关黑森行为的直觉，然后转到更大的电路，然后对数据进行培训。最后，我们展示了如何使用Hessian在训练变异电路期间调整更快收敛的学习率。
Machine learning techniques enhanced by noisy intermediate-scale quantum (NISQ) devices and especially variational quantum circuits (VQC) have recently attracted much interest and have already been benchmarked for certain problems. Inspired by classical deep learning, VQCs are trained by gradient descent methods which allow for efficient training over big parameter spaces. For NISQ sized circuits, such methods show good convergence. There are however still many open questions related to the convergence of the loss function and to the trainability of these circuits in situations of vanishing gradients. Furthermore, it is not clear how "good" the minima are in terms of generalization and stability against perturbations of the data and there is, therefore, a need for tools to quantitatively study the convergence of the VQCs. In this work, we introduce a way to compute the Hessian of the loss function of VQCs and show how to characterize the loss landscape with it. The eigenvalues of the Hessian give information on the local curvature and we discuss how this information can be interpreted and compared to classical neural networks. We benchmark our results on several examples, starting with a simple analytic toy model to provide some intuition about the behavior of the Hessian, then going to bigger circuits, and also train VQCs on data. Finally, we show how the Hessian can be used to adjust the learning rate for faster convergence during the training of variational circuits.
