耗散感知器量子神经网络的可训练性
Trainability of Dissipative Perceptron-Based Quantum Neural Networks
摘要：
已经提出了几种量子神经网络（QNN）的架构，其目标是在量子数据上有效地执行机器学习任务。对于特定的QNN结构，迫切需要严格的缩放结果，以了解哪些（如果有的话）将在大规模上可训练。在这里，我们分析了最近提出的一种称为耗散QNN（DQNN）的架构的梯度缩放（以及可训练性），其中每层的输入量子比特在层的输出处被丢弃。我们发现，DQNN可以表现出贫瘠的高原，即，量子位数呈指数级递减的梯度此外，我们在不同的条件下，如不同的成本函数和电路深度，DQNN的梯度的缩放提供定量界限，并表明可训练性并不总是得到保证。
英文摘要：
Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed.
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