论文标题
量子卷积神经网络中缺乏贫瘠的高原
Absence of Barren Plateaus in Quantum Convolutional Neural Networks
论文作者
论文摘要
量子神经网络（QNN）对有效分析量子数据的可能性产生了兴奋。但是，对于许多QNN建筑，存在指数式消失的梯度（称为贫瘠的高原景观），这种兴奋已经缓解了这种兴奋。最近，已经提出了量子卷积神经网络（QCNN），其中涉及一系列卷积和合并层，可减少码头数量，同时保留有关相关数据特征的信息。在这项工作中，我们严格分析QCNN体系结构中参数的梯度缩放。我们发现，梯度的方差不比多功能范围更快，这意味着QCNN不会表现出贫瘠的高原。这为随机初始化的QCNN的训练性提供了分析保证，该保证强调了QCNN在随机初始化下是可训练的，这与许多其他QNN架构不同。为了得出我们的结果，我们引入了一种基于图形的新方法，以分析对HAAR分布的单位者的期望值，这在其他情况下可能很有用。最后，我们执行数值模拟以验证我们的分析结果。
Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, Quantum Convolutional Neural Networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features. In this work we rigorously analyze the gradient scaling for the parameters in the QCNN architecture. We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. This provides an analytical guarantee for the trainability of randomly initialized QCNNs, which highlights QCNNs as being trainable under random initialization unlike many other QNN architectures. To derive our results we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts. Finally, we perform numerical simulations to verify our analytical results.
