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arXiv · 2510.13950

Quantum State Designs via Magic Teleportation

Hugo Lóio·Guglielmo Lami·Lorenzo Leone·Max McGinley·Xhek Turkeshi·Jacopo De Nardis
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Abstract

We investigate how non-stabilizer resources enable the emergence of quantum state designs within the projected ensemble. Starting from initial states with finite magic and applying resource-free Clifford circuits to scramble them, we analyze the ensemble generated by performing projective Pauli measurements on a subsystem of the final state. Using both analytical arguments and large-scale numerics, we show that the projected ensemble converges towards a state $k$-design with an error that decays exponentially with the $k$-th Stabilizer R\'enyi Entropy of the pre-measurement state, via a Magic-Induced Design Ansatz (MIDA) that we introduce. We identify a universal scaling form, valid across different classes of magic initial states, and corroborate it through numerical simulations and analytical calculations of the frame potential. For finite-depth Clifford unitaries, we show that the timescales at which state designs emerge are controlled by the transport of magic. We identify a ``magic teleportation'' mechanism whereby non-Clifford resources injected locally spread through Clifford scrambling and measurements across distances beyond the lightcone. Our results demonstrate how a small and controlled amount of magic suffices to generate highly random states, providing a systematic route toward generating quantum state designs in early fault-tolerant devices.

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Hugo Lóio, Guglielmo Lami, Lorenzo Leone, Max McGinley, Xhek Turkeshi, Jacopo De Nardis. 2025-10-15. Quantum State Designs via Magic Teleportation. https://arxiv.org/abs/2510.13950

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