Rodrigo Martínez-Peña

Lukas Gonon, Rodrigo Martínez-Peña, Juan-Pablo Ortega

Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for learning with noisy intermediate-scale quantum devices. Early experimental proposals, such as the restarting and rewinding protocols, relied on repeating previous steps of the quantum map to avoid backaction. However, this approach compromises real-time processing and increases computational overhead. Recent developments have introduced alternative protocols that address these limitations. These include online, mid-circuit measurement, and feedback techniques, which enable real-time computation while preserving the input history. Among these, the feedback protocol stands out for its ability to process temporal information with comparatively fewer components. Despite this potential advantage, the theoretical foundations of feedback-based quantum reservoir computing remain underdeveloped, particularly with regard to the universality and the approximation capabilities of this approach. This paper addresses this issue by presenting a recurrent quantum neural network architecture that extends a class of existing feedforward models to a dynamic, feedback-driven reservoir setting. We provide theoretical guarantees for variational recurrent quantum neural networks, including approximation bounds and universality results. Notably, our analysis demonstrates that the model is universal with linear readouts, making it both powerful and experimentally accessible. These results pave the way for practical and theoretically grounded quantum reservoir computing with real-time processing capabilities.

Rodrigo Martínez-Peña, Román Orús

Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems without requiring extensive parameter tuning. However, selecting and optimizing reservoir architectures remains an open problem. Next-generation reservoir computing simplifies this problem by employing nonlinear vector autoregression based on truncated Volterra series, thereby reducing hyperparameter complexity. Nevertheless, the latter suffers from exponential parameter growth in terms of the maximum monomial degree. Tensor networks offer a promising solution to this issue by decomposing multidimensional arrays into low-dimensional structures, thus mitigating the curse of dimensionality. This paper explores the application of a previously proposed tensor network model for predicting chaotic time series, demonstrating its advantages in terms of accuracy and computational efficiency compared to conventional echo state networks. Using a state-of-the-art tensor network approach enables us to bridge the gap between the tensor network and reservoir computing communities, fostering advances in both fields.