We investigate how nonstabilizer 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 toward a state $k$-design with an error that decays exponentially with the $k$th stabilizer Rényi entropy of the premeasurement state, via a magic-induced design ansatz (MIDA) that we introduce. We identify a scaling form that depends on the initial state only through its magic $M_k$, which we corroborate for distinct classes of initial states 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 light-cone. Our results demonstrate that an amount of magic scaling with the probed subsystem size, yet independent of the total system size, suffices to generate highly random states, providing a systematic route toward generating quantum state designs in early fault-tolerant devices.

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• Information scrambling
• Quantum circuits
• Quantum measurements
• Quantum simulation
• Quantum state engineering
• Quantum teleportation
• Quantum thermodynamics
• Resource theories