Absence of Barren Plateaus in Quantum Convolutional Neural Networks

By Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T. Sornborger, Patrick J. Coles. Physical Review X, 2020

389 citations recorded by the source corpus.

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 singles out QCNNs as being trainable 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ea9f31382c1b5b0c166bd1effc9feb7504899914

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Citations in the corpus

Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, methodology): “The barren plateaus phenomenon has also been studied in the context of quantum neural networks [41, 46, 103], and to the problem of learning scramblers [43].”
Variational quantum algorithms (2020, methodology): “[27, 176] an initialization strategy was developed specifically to address BPs in deep circuits.”
Quantum convolutional neural network for classical data classification (2021, background): “Variational quantum circuits with the hierarchical structure consisting of O(log(n)) layers do not exhibit the problem of “barren plateau” [30].”
VQE method: a short survey and recent developments (2021, background): “Despite these efforts, as well as more recent ones [75, 76, 77, 78, 79, 80], it is still too early to claim success since additional difficulties can come from hardware noise that can potentially modify the cost landscape associated with the parameter space.”
Barren plateaus in variational quantum computing (2024, neutral): “Similarly, the capacity of a PQC 82,83 — measured by how many functions it can represent — affects the concentration of the loss.”
Challenges and opportunities in quantum machine learning (2022, background): “Fortunately various strategies have been developed to address these barren plateaus, such as clever initialization [90], pre-training, and parameter correlation [82, 83].”
Quantum variational algorithms are swamped with traps (2022, positive): “The quantum convolutional neural network (QCNN) presents an interesting test bed for our analysis since it has been shown in prior work to avoid barren plateaus [47].”