Interpretable Quantum Advantage in Neural Sequence Learning

Abstract: Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, as we are able to pinpoint quantum contextuality as the source of this separation, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state of the art classical models even in practice.

• The paper demonstrates interpretable quantum advantage in neural sequence learning, showing that quantum contextuality provides an unconditional separation in memory efficiency, requiring only O(n) quantum qumodes vs. Omega(n^2) classical latent dimensions for the same task.
• It introduces Contextual Recurrent Neural Networks (CRNNs) that leverage quantum contextuality, outperforming classical models like GRUs and Transformers on both constructed contextual tasks and practical Spanish-to-English translation.
• The findings suggest a practical strategy for near-term quantum machine learning by extending simple classical models with minimal quantum features to harness task-specific contextual dependencies and achieve enhanced expressivity.

The paper "Interpretable Quantum Advantage in Neural Sequence Learning" addresses the challenge of identifying scenarios where quantum neural networks (QNNs) might offer a genuine advantage over classical models. Despite the theoretical potential of QNNs, existing studies often rely on complexity-theoretic assumptions without providing practical insights into their expressive power on classical data sets. The authors focus on elucidating the inherent advantages by analyzing the expressivity of QNNs in sequence learning tasks compared to their classical counterparts.

The study presents a comparative analysis between recurrent models based on Gaussian operations with non-Gaussian measurements and conventional neural network sequence models, such as linear recurrent neural networks (LRNNs). One central result is the identification of quantum contextuality as the pivotal resource enabling an unconditional separation in memory efficiency between quantum and classical models. The study provides evidence that contextual quantum models can express certain distributions with only $\operatorname{O}(n)$ qumodes, whereas classical models require an $\operatorname{\Omega}(n^2)$-dimensional latent space for the same task, resulting in superquadratic time complexity differences due to classical model scalability issues.

The paper introduces contextual recurrent neural networks (CRNNs), a class of QNNs capable of leveraging quantum contextuality for sequence learning. The CRNNs are examined on constructed tasks displaying quantum contextuality, demonstrating their superiority over trainable classical sequence models. The analysis is supported by showing that quantum contextuality in these models directly correlates with their enhanced expressivity.

Additionally, the authors extend the analysis to practical applications by evaluating CRNNs on a standard Spanish-to-English translation data set. Here, CRNNs demonstrate superior performance compared to state-of-the-art classical models, including GRUs and Transformers, under equivalent model sizes. This is attributed to the linguistic contextuality in translation tasks, which mirrors the quantum contextuality leveraged by CRNNs.

The paper suggests that the quantum advantage is not merely theoretical but has implications for real-world applications, particularly in tasks characterized by inherent contextual dependencies. The authors propose that the quantization of simple classical models, extended with minimal quantum features like non-Gaussian measurements, provides a fruitful strategy for the design of quantum machine learning models suitable for near-term quantum computing devices. This approach may circumvent the untrainable landscapes and significant resource demands of more general quantum architectures.

In conclusion, the study provides a rigorous demonstration of quantum contextuality as a resource for practical quantum advantages in machine learning and offers a pathway to explore task-specific quantum enhancements in model expressivity and computational efficiency.