Arbitrary Polynomial Separations in Trainable Quantum Machine Learning
<|reference_start|>Arbitrary Polynomial Separations in Trainable Quantum Machine Learning: 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.<|reference_end|>
@article{anschuetz2024arbitrary,
    title={Arbitrary Polynomial Separations in Trainable Quantum Machine Learning},
    author={Eric R. Anschuetz and Xun Gao},
    journal={arXiv preprint arXiv:2402.08606},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08606},
    primaryClass={quant-ph cs.LG}
}