Quantum State Designs via Magic Teleportation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914264644583424 |
|---|---|
| author | Lóio, Hugo Lami, Guglielmo Leone, Lorenzo McGinley, Max Turkeshi, Xhek De Nardis, Jacopo |
| author_facet | Lóio, Hugo Lami, Guglielmo Leone, Lorenzo McGinley, Max Turkeshi, Xhek De Nardis, Jacopo |
| contents | 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 Rényi 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum State Designs via Magic Teleportation Lóio, Hugo Lami, Guglielmo Leone, Lorenzo McGinley, Max Turkeshi, Xhek De Nardis, Jacopo Quantum Physics Statistical Mechanics 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 Rényi 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. |
| title | Quantum State Designs via Magic Teleportation |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2510.13950 |