Optimal quantum learning in proximity to universality

• URL: http://arxiv.org/abs/2510.18623v2
• Date: Wed, 22 Oct 2025 13:53:52 GMT
• Title: Optimal quantum learning in proximity to universality
• Authors: Moein N. Ivaki, Matias Karjula, Tapio Ala-Nissila,
• Abstract summary: boundary between classically simulable and computationally superior quantum systems is fundamental to identifying true quantum advantage.<n>We introduce a tunable $N$-qubit random circuit model, where a fraction $p$ of Clifford gates are probabilistically substituted with nonstabilizing conditional-$hatT$ gates.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The boundary between classically simulable and computationally superior quantum systems is fundamental to identifying true quantum advantage. 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 offer a general strategy for designing powerful and trainable quantum machine learning systems and clarify the physical resources underpinning quantum computational advantage.

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