Bence Hetényi, Benjamin J. Brown, Dominic. J. Williamson (Mar 06 2026).
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
∼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
O(d) depth of the Clifford measurement circuit, magic state cultivation becomes impractical for
d>5. Here, we perform logical
XS† 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.
