Expressibility-Enhancing Strategies for Quantum Neural Networks
This addresses a critical gap in quantum machine learning for researchers and practitioners, though it is incremental as it builds on existing QNN frameworks.
The paper tackles the problem that state-of-the-art quantum neural networks (QNNs) perform poorly in approximating simple sinusoidal functions, despite theoretical expressive power, and proposes four strategies that significantly enhance QNN performance in approximating complex multivariable functions while reducing circuit depth and qubits required.
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.