Absence of Barren Plateaus in Quantum Convolutional Neural Networks
This addresses a critical trainability issue for quantum machine learning practitioners, offering an analytical guarantee for QCNNs, though it is incremental as it builds on prior QCNN proposals.
The authors tackled the problem of exponentially vanishing gradients (barren plateaus) in quantum neural networks by analyzing the gradient scaling in Quantum Convolutional Neural Networks (QCNNs), finding that the gradient variance vanishes no faster than polynomially, implying QCNNs do not exhibit barren plateaus and are trainable under random initialization.
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.