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  • Open Access

Fold-transversal surface code cultivation

Kaavya Sahay*,†, Pei-Kai Tsai*, Kathleen (Katie) Chang*, Qile Su, Thomas B. Smith, Shraddha Singh‡, and Shruti Puri

  • *These authors contributed equally to this work.
  • †Contact author: kaavya.sahay@yale.edu
  • ‡Present address: IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA.
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PRX Quantum 7, 033006 – Published 7 July, 2026

DOI: https://doi.org/10.1103/gpvl-lg4c

Abstract

Magic state cultivation is a state-of-the-art protocol to prepare ultra-high fidelity non-Clifford resource states for universal quantum computation. It offers a significant reduction in spacetime overhead compared to traditional magic state distillation techniques. Cultivation protocols involve measuring a transversal logical Clifford operator on an initial small-distance code and then rapidly growing to a larger-distance code. In this work, we present a new cultivation scheme in which we measure the fold-transversal Hadamard of the unrotated surface code, and leverage unitary techniques to grow within the surface code family. Using both stabilizer and state vector simulations we find that this approach achieves the lowest known spacetime overhead for magic state cultivation. Practical implementation of our protocol is best suited to architectures with nonlocal connectivity, showing the strength of architectures where such connectivity is readily available.

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Popular Summary

The efficient preparation of high-quality non-Clifford “magic” states has presented a significant challenge to the field of fault-tolerant quantum computation. New techniques for magic state cultivation have dramatically reduced this overhead in terms of both qubit count and time taken. These techniques involve the careful use of logical checks, postselection, and growth of encoded magic states. In this work, we propose a new cultivation scheme aided by long-range entangling gates to prepare magic states with extremely low error rates within the surface code, a particularly popular encoding choice for practical quantum computation. At the core of our cultivation strategy is the fault-tolerant measurement of a fold-transversal operator available to the surface code. By careful design of each cultivation stage, we significantly reduce both the qubit and time overhead required to prepare high-quality states compared to state-of-the-art methods.

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Outline

Information

PRX Quantum 7, 033006– Published 7 July, 2026
  • Received 6 October 2025
  • Revised 4 March 2026
  • Accepted 17 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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