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Efficient Magic State Cultivation on RP2

Zi-Han Chen1,2,3,*, Ming-Cheng Chen1,2,3,†, Chao-Yang Lu1,2,3,‡, and Jian-Wei Pan1,2,3,§

  • *Contact author: czh007@mail.ustc.edu.cn
  • †Contact author: cmc@ustc.edu.cn
  • ‡Contact author: cylu@ustc.edu.cn
  • §Contact author: pan@ustc.edu.cn
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PRX Quantum 7, 010315 – Published 22 January, 2026

DOI: https://doi.org/10.1103/9kys-3whh

Abstract

Preparation of high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among previous attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC) [Gidney et al., Magic state cultivation: growing T states as cheap as CNOT gates, arXiv:2409.17595], a recently proposed protocol for logical T state preparation without magic state distillation, achieves state-of-the-art efficiency. Inspired by this work [Gidney et al., Magic state cultivation: growing T states as cheap as CNOT gates, arXiv:2409.17595], we propose a MSC procedure that can produce logical T states on the rotated surface code at a further reduced cost. To maintain high efficiency throughout our protocol, we design structured codes along with compact circuits bridging between them. More specifically, we construct a code family, the RP code, by putting the rotated surface code on RP2 (a two-dimensional manifold), as well as two self-dual Calderbank-Shor-Steane codes, named SRP-3 and SRP-5, respectively. In our MSC protocol, we start with a cultivation process, in which a high-fidelity T state is prepared on a small RP code with distance 3 or 5. Then, to preserve the logical T state, we use an efficient and easy-to-decode expansion stage to grow a small RP code to a larger rotated surface code in one syndrome extraction (SE) round. The RP code serves as an efficient transfer station with efficient SE circuits and compact interfaces between the SRP-3 (or SRP-5) code—used in the cultivation process to efficiently verify the correctness of the logical T state—and larger rotated surface codes for preserving the prepared logical T state. Our MSC protocol utilizes nonlocal connectivity, available on both neutral atom array and ion trap platforms. According to our Monte Carlo sampling results, our MSC protocol requires about an order of magnitude smaller space-time volume to reach a target logical error rate of around 10−9 compared to the original MSC protocol.

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Physics Subject Headings (PhySH)

Popular Summary

Implementation of quantum algorithms at a practically relevant scale requires quantum operations at an error rate far lower than what is currently achievable on physical qubits. By encoding qubits into quantum error correcting (QEC) codes, we can achieve better protection from noise on these (logical) qubits than on their physical counterparts. Among crucial gadgets for implementing universal quantum operations on logical qubits, preparation of high-fidelity logical magic states is especially costly. This work presents a protocol that leverages nonlocal connectivity to produce logical magic states on the rotated surface code (RSC)—a popular, hardware-friendly QEC code—with significantly reduced cost compared to previous results.

Inspired by a state-of-the-art protocol, magic state cultivation (MSC), which prepares logical magic states on the color code by measuring a specific logical Clifford operator, the authors propose an alternative MSC protocol for the RSC with up to an order of magnitude reduction in space-time cost compared to the original MSC protocol. The authors codesigned codes with special structures—including a variant of the RSC on a nonorientable surface—with compact circuits as code interfaces. On the basis of this, the authors composed their MSC protocol, with high efficiency throughout, by tightly knitting together high-performance circuits on the designed codes.

Exploring and optimizing the use of this MSC protocol inside a large-scale quantum computation—such as interfacing with other gadgets for logical operations—is an important future direction.

Article Text

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Outline

Information

PRX Quantum 7, 010315– Published 22 January, 2026
  • Received 4 August 2025
  • Revised 15 October 2025
  • Accepted 19 November 2025
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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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