Quantum Convolutional Neural Network with Nonlinear Effects and Barren Plateau Mitigation

TL;DR

This paper introduces a quantum convolutional neural network architecture that incorporates nonlinear effects and mitigates barren plateaus, demonstrating high accuracy on standard datasets and validating its quantum fidelity.

Contribution

It presents a novel QCNN design that integrates classical convolutional concepts with quantum operations, addressing key challenges in quantum neural network scalability and expressiveness.

Findings

Achieved 99.0% test accuracy on MNIST

Achieved 88.0% test accuracy on Fashion-MNIST

Validated quantum fidelity through simulation comparisons

Abstract

Quantum neural networks (QNNs) leverage quantum entanglement and superposition to enable large-scale parallel linear computation, offering a potential solution to the scalability limits of classical deep learning. However, their practical deployment is hampered by two key challenges: the lack of intrinsic nonlinear operations and the barren plateau phenomenon. We propose a quantum convolutional neural network (QCNN) architecture that simultaneously addresses both issues. Nonlinear effects are introduced via orthonormal basis expansions of power series, while barren plateaus are mitigated by directly parameterizing unitary matrices rather than stacking multiple parameterized gates. Our design further incorporates quantum analogs of convolutional kernels and strides for scalable circuit construction. Experiments on MNIST and Fashion-MNIST datasets achieve 99.0% and 88.0% test accuracy, respectively. Consistency between PyTorch-based matrix simulation and Qiskit-based quantum circuit simulation validates the physical fidelity of the model. These results demonstrate a flexible and effective quantum architecture that faithfully integrates classical convolutional mechanisms into a quantum framework, paving the way for practical and expressive QNNs.