Quantum State Designs via Magic Teleportation
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 -design with an error that decays exponentially with the -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.
Cite
@article{arxiv.2510.13950,
title = {Quantum State Designs via Magic Teleportation},
author = {Hugo Lóio and Guglielmo Lami and Lorenzo Leone and Max McGinley and Xhek Turkeshi and Jacopo De Nardis},
journal= {arXiv preprint arXiv:2510.13950},
year = {2026}
}