Expressibility-Enhancing Strategies for Quantum Neural Networks

• URL: http://arxiv.org/abs/2211.12670v2
• Date: Tue, 16 May 2023 04:05:25 GMT
• Title: Expressibility-Enhancing Strategies for Quantum Neural Networks
• Authors: Yalin Liao, Junpeng Zhan
• Abstract summary: Quantum neural networks (QNNs) can be trained to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of QNNs. We propose four expressibility-enhancing strategies for QNNs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of QNNs. However, in almost all literature, QNNs' expressive power is numerically validated using only simple univariate functions. We surprisingly discover that state-of-the-art QNNs with strong expressive power can have poor performance in approximating even just a simple sinusoidal function. To fill the gap, we propose four expressibility-enhancing strategies for QNNs: Sinusoidal-friendly embedding, redundant measurement, post-measurement function, and random training data. We analyze the effectiveness of these strategies via mathematical analysis and/or numerical studies including learning complex sinusoidal-based functions. Our results from comparative experiments validate that the four strategies can significantly increase the QNNs' performance in approximating complex multivariable functions and reduce the quantum circuit depth and qubits required.

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