Harnessing complex quantum dynamics for reservoir computing

Quantum technologies are rapidly evolving toward regimes where controllable quantum dynamics can be exploited for information processing, simulation, and machine learning. Within this landscape, quantum reservoir computing (QRC) has emerged as an appealing paradigm: it harnesses the high-dimensional dynamics of quantum systems to perform temporal tasks with minimal training overhead, making it particularly well suited for current noisy intermediate-scale quantum devices. In parallel, modern perspectives on quantum many-body systems reveal that tools such as complex-network theory and spectral methods can uncover structures in quantum states and dynamics that remain hidden to conventional approaches. This thesis brings these threads together. It explores how \textit{quantum statistics, many-body correlations, chaoticity, and metastability} shape information processing in QRC. Furthermore, we have also demonstrated how network-theoretic methods can reveal new features of strongly correlated phases.

This thesis contributes to the emerging field of quantum reservoir computing by examining how different physical models shape the learning capabilities of quantum reservoirs. Each article investigates a distinct class of systems: simple hopping networks governed by particle statistics, interacting atomic lattices described by the Bose–Hubbard model, driven-dissipative oscillators exhibiting metastability. Through these diverse settings, a central goal is to identify which physical ingredients enhance the performance of QRC. To address these questions, we combine analytical insights with a broad range of numerical techniques, including exact diagonalization, tensor-network simulations, and open-system dynamics. Together, these approaches provide a unified framework for understanding how quantum dynamics can be exploited for computation.

The main findings of the thesis on QRC and complex networks can be summarized as follows. (i) Particle statistics fundamentally shape computational power: fermions exhibit superior information spreading due to their algebra, while bosons can outperform all other substrates when input encoding is optimized. (ii) Metastability constitutes a computational resource: long-lived metastable states enhance memory capacity and allow a fast-injection protocol. (iii) In atomic lattices described by the Bose–Hubbard model, QRC performance is governed by the interplay between interactions and tunneling, with optimal regimes appearing both in the weakly interacting limit and near the onset of quantum chaos; importantly, disorder is not required to achieve high performance. (iv) Complex-network analysis reveals hidden features of the Kitaev chain: network observables sharply detect the topological transition in the Kitaev chain and uncover a previously unnoticed fully connected, perfectly clustered regime linked to ground-state factorization observed in the Ising spin chain.

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