Exact logical error rates for magic state cultivation

arXiv:2609.18922 · quant-ph · Submitted 2026-09-16 · Read on arXiv

quant-ph

Submitted: 2026-09-16

Updated: 2026-09-29

Comments: v3 - expanded section on Pauli semiwebs and implementation available at: https://github.com/kh428/exact_ler_for_msc

Code: https://github.com/mjsutcliffe99/ParamZX

License: http://creativecommons.org/licenses/by/4.0/

The gist: We compute exactly the acceptance and logical error rates for the distance d=3 and d=5 magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli

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Abstract

We compute exactly the acceptance and logical error rates for the distance d=3 and d=5 magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual T-gates are studied, not the S-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths (p). We provide a series expansion form to the logical error rates, through order (p/(1-p)) 10. The analytical results recover the numerical values from Clifft and SOFT at both d=3 and d=5 to within their sampling uncertainty. Then, we show that the d=3 and d=5 circuits actually have fault distances of d fault=2 and d fault=3 respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].

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