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High Rate Magic State Cultivation on the Surface Code

Yotam Vaknin1,2,*, Shoham Jacoby1,2, Arne Grimsmo1, and Alex Retzker1,2

  • *Contact author: yotam.vaknin@mail.huji.ac.il
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PRX Quantum 7, 010353 – Published 16 March, 2026

DOI: https://doi.org/10.1103/p8tw-6kq9

Abstract

Magic state cultivation is a leading approach for generating the resource states required for fault-tolerant quantum computation. Here we present a cultivation protocol that increases the success probability of magic state generation in platforms with flexible and nonlocal connectivity. Our method implements cultivation directly on the surface code, avoiding the detour through alternative, less efficient error-correcting codes used in prior approaches. This both improves the acceptance rate and preserves compatibility with the geometry of the code and the hardware. Numerical simulations show that our protocols improve success probabilities and reduce output error rates compared with protocols tailored to locally connected platforms. Under realistic noise models for cold-atom and trapped-ion systems, we improve the rate of magic state generation by more than a factor of 20. Finally, we study qubit loss and erasure and show that very low error rates can be achieved with minimal overhead, reaching below 10−6 infidelity using only nine physical erasure qubits.

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Popular Summary

We investigate a quantum computation technique called magic state cultivation. Generating high-fidelity magic states is a critical challenge for fault-tolerant quantum computing. We implement this procedure directly on surface codes, improving its success rate and fidelity. We also describe a measurement protocol for generating a different type of resource state known as the CX state.

Our proposed protocol utilizes transversal gates composed of three-qubit and operations across pairs of quantum error-correcting codes. This technique is particularly well suited to quantum computing platforms based on Rydberg atoms and trapped ions, which offer flexible, all-to-all qubit connectivity. We demonstrate that cultivation on the surface code improves both the yield and fidelity of the generated magic states.

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Outline

Information

PRX Quantum 7, 010353– Published 16 March, 2026
  • Received 10 February 2025
  • Revised 6 October 2025
  • Accepted 23 January 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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