verified 3 stabilizer terms reproduce |cat_6>, checked symbolically
Implied per-copy exponent γ ≤ 0.3962 against a published 0.3962 through the implied H-type exponent log₂χ(catm)/(m−2), no improvement.
χ(|cat6⟩) ≤ 3 from |cat6⟩ = 2^{-3/2}(|0^6> - i|1^6>) + 2^{-1/2} e^{3 i π/4}(|E6⟩ + i|K6⟩), |E6⟩ the uniform superposition of the even-weight strings and |K6⟩ = prod_{i<j} CZ_ij |E6⟩ (Qassim, Pashayan, and Gosset, Eq. 5). Through χ(T^6) ≤ 2 χ(cat_6) this is the rank-6 cell of the qubit_H orbit, bounds/qubit_H-m6-upper-6.json. Exact with the appendix's χ(cat_6) ≥ χ(cat_5) > 2, cited in bounds/cat-m6-lower-3.json. Witness built by research/constructions/qpg_cat.py from the three terms as written, and verified in exact arithmetic. Implied H-type exponent log_2(3)/4 = 0.3963, the published qubit exponent.
Qassim, Pashayan, and Gosset · arXiv:2106.07740 · literature
{
"schema_version": "0.1",
"orbit": "cat",
"m": 6,
"direction": "upper",
"rank": 3,
"provenance": {
"author": "Qassim, Pashayan, and Gosset",
"reference": "arXiv:2106.07740",
"method": "literature",
"date": "2021-06-14",
"github": []
},
"notes": "chi(|cat_6>) <= 3 from |cat_6> = 2^{-3/2}(|0^6> - i|1^6>) + 2^{-1/2} e^{3 i pi/4}(|E_6> + i|K_6>), |E_6> the uniform superposition of the even-weight strings and |K_6> = prod_{i<j} CZ_ij |E_6> (Qassim, Pashayan, and Gosset, Eq. 5). Through chi(T^6) <= 2 chi(cat_6) this is the rank-6 cell of the qubit_H orbit, bounds/qubit_H-m6-upper-6.json. Exact with the appendix's chi(cat_6) >= chi(cat_5) > 2, cited in bounds/cat-m6-lower-3.json. Witness built by research/constructions/qpg_cat.py from the three terms as written, and verified in exact arithmetic. Implied H-type exponent log_2(3)/4 = 0.3963, the published qubit exponent.",
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