Efficient Magic State Cultivation for $\sqrt{T}$ Gates

I-Chi Chen; Matheus da Silva Fonseca; Andrew Sornborger

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arXiv · 2606.10430

Efficient Magic State Cultivation for $\sqrt{T}$ Gates

I-Chi Chen·Matheus da Silva Fonseca·Andrew Sornborger

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Abstract

Recently, experimental and theoretical quantum error correction methodology has seen remarkable breakthroughs. In particular, magic state cultivation has been shown to simplify magic-state preparation and make it feasible for near-term devices. However, recent research on magic state cultivation has focused primarily on the cultivation of $T\left| + \right>_L$. Only a few other magic state cultivation methods beyond $T\left| + \right>_L$ have been investigated. Here, we generalize phase kickback checks for magic states at arbitrary Clifford hierarchy levels in specific codes. We provide an example of cultivation of $\sqrt{T}\left| + \right>_L$ in the doubled color code and the corresponding escape strategy using lattice surgery from the color code to large rotated surface codes. Using state vector simulation for un-grown cultivation, we observe a strong consistence between $S\left| + \right>_L$ and $\sqrt{T}\left| + \right>_L$ cultivation's performance on the doubled color code. Finally, we discuss the application of the corresponding $\sqrt{T}\left| + \right>_L$ cultivation, incorporating the STAR architecture and $T$ gates, for early fault-tolerant quantum computing and its potential to shorten gate synthesis in the fully fault-tolerant quantum computing era.

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I-Chi Chen, Matheus da Silva Fonseca, Andrew Sornborger. 2026-06-09. Efficient Magic State Cultivation for $\sqrt{T}$ Gates. https://arxiv.org/abs/2606.10430

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