Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks in performing a classical sequence modeling task. Furthermore, each unit cell of the introduced class of QNNs is computationally efficient, implementable in constant time on a quantum device. The classical networks we prove a separation over include well-known examples such as recurrent neural networks and Transformers. We show that quantum contextuality is the source of the expressivity separation, suggesting that other classical sequence learning problems with long-time correlations may be a regime where practical advantages in quantum machine learning may exist.

翻译：近期量子机器学习的理论结果表明，量子神经网络（QNNs）的表达能力与其可训练性之间存在普遍权衡；作为这些结果的推论，人们认为实际中QNN相对于经典机器学习模型在表达能力上实现指数级分离是不可行的，因为此类QNN的训练时间随模型规模呈指数增长。我们在此通过构建一个高效可训练的QNN层次结构来规避这些负面结果，该结构在执行经典序列建模任务时，能够无条件地证明相对于经典神经网络具有任意恒定次数的多项式内存分离。此外，所引入的QNN类中的每个单元都在计算上高效，可在量子设备上以恒定时间实现。我们证明与之分离的经典网络包括众所周知的实例，如循环神经网络和Transformer。我们表明量子语境性是表达能力分离的根源，这暗示其他具有长时间相关性的经典序列学习问题可能是量子机器学习存在实际优势的领域。