Matias Karjula | Searcharxiv

arXiv2026

The ebbs and flows of quantum learning and sensing

What is the relation between subsystem quantum complexity and the emergence of computationally useful structure? We address this by studying a family of minimally tunable postvariational quantum circuits, and show how spectral nonflatness and metrological response directly control the ensemble-typical information processing power. This unveils an intermediate "learning phase" that precedes the onset of quantum chaos, characterized by pronounced nonflatness and sensitivity of readout states. The optimal information processing capacity improves with system size, while deep scrambling suppresses observable response. The results reveal how such features of random quantum dynamics can be viewed as computational resources for scalable nonlinear computation.

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arXiv2025

Optimal quantum reservoir learning in proximity to universality

The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this within the framework of quantum reservoir computing by introducing a tunable $N$-qubit random circuit model, where a fraction $p$ of Clifford gates are probabilistically substituted with nonstabilizing conditional-$\hat{T}$ gates. We establish a direct correspondence between the reservoir's performance on temporal processing tasks and its entanglement spectrum statistics and long-range nonstabilizer resource content. To assess scalability, we study the scaling of the anti-flatness of states in the large-$N$ limit at a fixed circuit depth ratio $d/N \sim \mathcal{O}(1)$. This is taken as a witness to concentration of measures, a known impediment to learning in thermalizing systems. We demonstrate that the learnability and scalability of the reservoir can be continuously controlled by the parameter $p$, allowing us to navigate from classically tractable to maximally expressive quantum dynamics. These architecture-agnostic results provide a general strategy for designing tunable and expressive quantum reservoirs, highlighting how certain nonclassical properties control average-case intrinsic learnability and functionality.

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