Quantum Convolutional Neural Networks

Abstract

Neural network-based machine learning has recently proven successful for many complex applications ranging from image recognition to precision medicine. However, its direct application to problems in quantum physics is challenging due to the exponential complexity of many-body systems. Motivated by recent advances in realizing quantum information processors, we introduce and analyze a quantum circuit-based algorithm inspired by convolutional neural networks, a highly effective model in machine learning. Our quantum convolutional neural network (QCNN) uses only O(log(N)) variational parameters for input sizes of N qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. To explicitly illustrate its capabilities, we show that QCNN can accurately recognize quantum states associated with a 1D symmetry-protected topological phase, with performance surpassing existing approaches. We further demonstrate that QCNN can be used to devise a quantum error correction scheme optimized for a given, unknown error model that significantly outperforms known quantum codes of comparable complexity. Finally, potential experimental realizations and generalizations of QCNN are discussed.