Constant-depth magic state cultivation with Clifford measurements by gauging

Abstract:Magic states are a scarce resource for two-dimensional qubit stabilizer codes. Magic state cultivation was recently proposed to reduce the cost of magic state preparation by measuring the transversal Clifford operator of the color code. Cultivation achieves $\sim 10^{-9}$ logical error rates for the $d=5$ color code, with substantially lower space-time overhead than magic state distillation. However, due to the $\mathcal{O}(d)$ depth of the Clifford measurement circuit, magic state cultivation becomes impractical for $d>5$. Here, we perform logical $XS^\dagger$ measurements on the color code by gauging a transversal Clifford gate, resulting in a constant-depth logical measurement circuit. We employ repeated gauging measurements with post-selection rather than performing error correction on the Clifford stabilizer code that emerges during the gauging protocol, thus gaining simplicity at the cost of scalability. Our protocol requires a regular square grid connectivity and yields logical error rates comparable to magic state cultivation. The $d=7$ version of our protocol gives access to the $10^{-12}$ logical error rate regime at $0.05\%$ physical error rate while retaining more than $1\%$ of the shots after the equivalent of the cultivation stage.

arXiv:2603.05429 [quant-ph]

(or arXiv:2603.05429v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.05429 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. Lett. 137, 140601 (2026)

https://doi.org/10.1103/f7fz-6zsy Focus to learn more DOI(s) linking to related resources

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