verified 15 stabilizer terms reproduce |qubit_T>^{ot 10}, checked symbolically
Implied per-copy exponent γ ≤ 0.3907 against a published 0.3962, an improvement.
1 run; 0.001 CPU-hours; 0.001 h wall-clock; on direct construction, no search.
Eq. (8) of S. Bevins, 'A three-eighths upper bound on the stabilizer-rank exponent of face-center magic states'. With v = a + z b, z = (1 + i √ 3)/2, and c = a + b, v^(x5) is a sum of fifteen words in a, b, c. The dictionary L(a) = (i, i, i, -i), L(b) = (1 - i, 0, 0, 1 + i), L(c) = (1, i, i, 1) sends each letter to a two-qubit stabilizer state, and f ⊗ f = kappa L(v) for f proportional to |T⟩, so each word is a ten-qubit stabilizer state and χ(|T⟩⊗10) ≤ 15, exponent 0.3907. The paper glues this identity with its image under a symmetry into 24 terms at m = 12 and builds a substitution giving γ ≤ 3/8; those cells are above the board's m ≤ 10 cap. Terms converted with verify_challenge/to_witness.py, coefficients exact.
Samuel Bevins · arxiv:2610.17500 · structured construction from a fifteen-word identity
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"coeffs": [
"-2/9 + 2*sqrt(3)/9 + I*(2/9 + 2*sqrt(3)/9)",
"4*sqrt(2)/9",
"-2/9 + 2*sqrt(3)/9 + I*(-2*sqrt(3)/9 - 2/9)",
"2*sqrt(3)/27 + 2/9 + I*(2/9 - 2*sqrt(3)/27)",
"2*sqrt(3)/27 + 2/9 + I*(2/9 - 2*sqrt(3)/27)",
"2*sqrt(6)/27 + 2*sqrt(2)*I/9",
"2*sqrt(6)/27 + 2*sqrt(2)*I/9",
"4*sqrt(3)/27 + 4*sqrt(3)*I/27",
"4*sqrt(3)/27 + 4*sqrt(3)*I/27",
"4*sqrt(3)/27 - 4*sqrt(3)*I/27",
"4*sqrt(3)/27 - 4*sqrt(3)*I/27",
"2*sqrt(3)/27 + 2/9 + I*(-2/9 + 2*sqrt(3)/27)",
"2*sqrt(3)/27 + 2/9 + I*(-2/9 + 2*sqrt(3)/27)",
"2*sqrt(6)/27 - 2*sqrt(2)*I/9",
"2*sqrt(6)/27 - 2*sqrt(2)*I/9"
]
},
"provenance": {
"author": "Samuel Bevins",
"reference": "arxiv:2610.17500",
"method": "structured construction from a fifteen-word identity",
"date": "2026-10-12",
"github": [
"sjbevins"
],
"compute": {
"cpu_hours": 0.001,
"wall_clock_hours": 0.001,
"runs": 1,
"hardware": "direct construction, no search"
}
},
"notes": "Eq. (8) of S. Bevins, 'A three-eighths upper bound on the stabilizer-rank exponent of face-center magic states'. With v = a + z b, z = (1 + i sqrt 3)/2, and c = a + b, v^(x5) is a sum of fifteen words in a, b, c. The dictionary L(a) = (i, i, i, -i), L(b) = (1 - i, 0, 0, 1 + i), L(c) = (1, i, i, 1) sends each letter to a two-qubit stabilizer state, and f (x) f = kappa L(v) for f proportional to |T>, so each word is a ten-qubit stabilizer state and chi(|T>^10) <= 15, exponent 0.3907. The paper glues this identity with its image under a symmetry into 24 terms at m = 12 and builds a substitution giving gamma <= 3/8; those cells are above the board's m <= 10 cap. Terms converted with verify_challenge/to_witness.py, coefficients exact."
}