Absence of Barren Plateaus in Quantum Convolutional Neural Networks

2020/11/30 by Arthur Pesah, M. Cerezo, Samson Wang +4 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Computer science #Convolutional neural network #Graph #Mathematics #Physics #Pooling #Quantum #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Quantum mechanics #Qubit #Scaling #Statistical physics #Stochastic Gradient Optimization Techniques #Theoretical computer science #cs.LG #quant-ph #stat.ML

paper · pdf · doi:10.1103/physrevx.11.041011

published as Phys. Rev. X 11, 041011 (2021) · 9 + 20 pages, 7 + 8 figures, 3 tables. Updated to published version

openalex publication_date 2021/10/15 · arxiv created 2021/11/01 · arxiv updated 2021/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 result 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.

Citations

• Learning representations by back-propagating errors
• A Quantum Approximate Optimization Algorithm
• The quest for a Quantum Neural Network
• An introduction to quantum machine learning
• Gradient-based learning applied to document recognition
• A variational eigenvalue solver on a photonic quantum processor
• Quantum Machine Learning
• Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review
• Quantum Convolutional Neural Networks
• Evaluating analytic gradients on quantum hardware
• Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
• Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation
• Toward Trainability of Quantum Neural Networks

Cited by

• Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark
• Simulating Nonlinearity in Quantum Neural Networks While Mitigating Barren Plateaus