量子启发的激活函数与量子切比雪夫多项式网络
Quantum-inspired activation functions and quantum Chebyshev-polynomial network
AI总结：
本文研究量子启发激活函数在神经网络中的作用，提出混合量子切比雪夫多项式网络QCPN，证明三层QCPN可逼近任意连续函数，并展示其在减少训练步数和模型深度方面的优势。
摘要：
受量子计算所提供的显著优势驱动，量子机器学习的研究近年来不断增加。尽管量子机器学习在某些应用中已经展示了量子加速，但对其性能提升背后机制的全面理解仍然难以捉摸。本研究通过考察集成在卷积神经网络（CNN）中的量子电路的功能可表达性来解决这一问题。通过在MNIST、Fashion MNIST和Letter数据集上的数值实验，我们的混合量子-经典CNN模型展示了更优越的特征选择能力，并且与经典CNN相比大幅减少了所需的训练步数。值得注意的是，我们观察到在经典神经网络中引入另外三种量子启发的激活函数时也取得了类似的性能提升，这表明采用量子启发激活函数具有益处。此外，我们基于量子激活函数的性质开发了一种混合量子切比雪夫多项式网络（QCPN）。我们证明一个三层QCPN可以逼近任意连续函数，而这是标准三层经典神经网络无法实现的。我们的研究结果表明，量子启发的激活函数可以在保持高学习能力的同时减少模型深度，使其成为优化大规模机器学习模型的一种有前景的方法。我们还概述了未来在机器学习中利用量子优势的研究方向，旨在进一步释放这一快速发展领域的潜力。
英文摘要：
Driven by the significant advantages offered by quantum computing, research in quantum machine learning has increased in recent years. While quantum speed-up has been demonstrated in some applications of quantum machine learning, a comprehensive understanding of its underlying mechanisms for improved performance remains elusive. Our study address this problem by investigating the functional expressibility of quantum circuits integrated within a convolutional neural network (CNN). Through numerical experiments on the MNIST, Fashion MNIST, and Letter datasets, our hybrid quantum-classical CNN model demonstrates superior feature selection capabilities and substantially reduces the required training steps compared to classical CNNs. Notably, we observe similar performance improvements when incorporating three other quantum-inspired activation functions in classical neural networks, indicating the benefits of adopting quantum-inspired activation functions. Additionally, we developed a hybrid quantum Chebyshev-polynomial network (QCPN) based on the properties of quantum activation functions. We demonstrate that a three-layer QCPN can approximate any continuous function, a feat not achievable by a standard three-layer classical neural network. Our findings suggest that quantum-inspired activation functions can reduce model depth while maintaining high learning capability, making them a promising approach for optimizing large-scale machine-learning models. We also outline future research directions for leveraging quantum advantages in machine learning, aiming to unlock further potential in this rapidly evolving field.
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