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  • Letter
  • Open Access

Optimal quantum reservoir learning in proximity to universality

Moein N. Ivaki1,*, Matias Karjula1, and Tapio Ala-Nissila1,2,†

  • 1MSP Group, Department of Applied Physics, Aalto University, FI-00076 Aalto, Espoo, Finland
  • 2Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom

  • *Contact author: moein.najafiivaki@aalto.fi
  • †Contact author: tapio.ala-nissila@aalto.fi
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Phys. Rev. A 113, L060401 – Published 1 June, 2026

DOI: https://doi.org/10.1103/tnfv-lzfx

Abstract

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-T̂ 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 antiflatness of states in the large-N limit at a fixed circuit depth ratio d/N∼O(1). This is taken as a witness to the 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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Phys. Rev. A 113, L060401– Published 1 June, 2026
  • Received 22 October 2025
  • Revised 22 December 2025
  • Accepted 13 May 2026
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