Randomness-enhanced expressivity of quantum neural networks

Abstract

As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum (NISQ) devices. Conventional QNNs are described by parametrized quantum circuits, which perform unitary operations and measurements on quantum states. In this work, we propose a novel approach to enhance the expressivity of QNNs by incorporating randomness into quantum circuits. Specifically, we introduce a random layer, which contains single-qubit gates sampled from an trainable ensemble pooling. The prediction of QNN is then represented by an ensemble average over a classical function of measurement outcomes. We prove that our approach can accurately approximate arbitrary target operators using Uhlmann's theorem for majorization, which enables observable learning. Our proposal is demonstrated with extensive numerical experiments, including observable learning, Rényi entropy measurement, and image recognition. We find the expressivity of QNNs is enhanced by introducing randomness for multiple learning tasks, which could have broad application in quantum machine learning.

arXiv comment6 pages, 4 figures

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• Nonstabilizerness via matrix product states in the Pauli basis
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• Variational Tensor Neural Networks for Deep Learning
• Variational measurement-based quantum computation for generative modeling
• Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs
• Machine-Learning Insights into the Entanglement-trainability Correlation of Parameterized Quantum Circuits
• Channel Attention for Quantum Convolutional Neural Networks
• Measuring Incompatible Observables with Quantum Neural Networks