Absence of Barren Plateaus in Quantum Convolutional Neural Networks
Autor: | Marco Cerezo, Tyler Volkoff, Samson Wang, Andrew T. Sornborger, Arthur Pesah, Patrick J. Coles |
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Jazyk: | angličtina |
Rok vydání: | 2021 |
Předmět: |
Physics
FOS: Computer and information sciences Quantum Physics Computer Science - Machine Learning Quantitative Biology::Neurons and Cognition Artificial neural network QC1-999 Computer Science::Neural and Evolutionary Computation General Physics and Astronomy FOS: Physical sciences Machine Learning (stat.ML) Convolutional neural network Machine Learning (cs.LG) Statistics - Machine Learning Limit (mathematics) Statistical physics Quantum Physics (quant-ph) Quantum |
Zdroj: | Physical Review X, Vol 11, Iss 4, p 041011 (2021) |
ISSN: | 2160-3308 |
Popis: | 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. Comment: 9 + 20 pages, 7 + 8 figures, 3 tables. Updated to published version |
Databáze: | OpenAIRE |
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