verified 18 stabilizer terms reproduce |qubit_T>^{ot 10}, checked symbolically
Implied per-copy exponent γ ≤ 0.4170 against a published 0.3962, no improvement.
1 run; 0.001 CPU-hours; 0.001 h wall-clock; on Apple silicon laptop, one core; direct construction, no search.
Tensor product of the board's witnesses qubit_T-m4-upper-3.json, qubit_T-m4-upper-3.json, qubit_T-m2-upper-2.json: χ(|qubitT⟩⊗4) ≤ 3 x χ(|qubitT⟩⊗4) ≤ 3 x χ(|qubitT⟩⊗2) ≤ 2 gives χ(|qubitT⟩⊗10) ≤ 18, exponent 0.4170. First witness for this cell; it is the sub-multiplicative value the board already implied and does not move the exponent. Terms are the exact products (x0 and l concatenated, W and Q block diagonal) and coefficients the exact products, built by research/constructions/product_witness.py.
this repository · stabrank research/constructions/product_witness.py · structured construction
{
"schema_version": "0.1",
"orbit": "qubit_T",
"m": 10,
"direction": "upper",
"rank": 18,
"provenance": {
"author": "this repository",
"reference": "stabrank research/constructions/product_witness.py",
"method": "structured construction",
"date": "2026-09-22",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.001,
"wall_clock_hours": 0.001,
"runs": 1,
"hardware": "Apple silicon laptop, one core; direct construction, no search"
}
},
"notes": "Tensor product of the board's witnesses qubit_T-m4-upper-3.json, qubit_T-m4-upper-3.json, qubit_T-m2-upper-2.json: chi(|qubit_T>^4) <= 3 x chi(|qubit_T>^4) <= 3 x chi(|qubit_T>^2) <= 2 gives chi(|qubit_T>^10) <= 18, exponent 0.4170. First witness for this cell; it is the sub-multiplicative value the board already implied and does not move the exponent. Terms are the exact products (x0 and l concatenated, W and Q block diagonal) and coefficients the exact products, built by research/constructions/product_witness.py.",
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"coeffs": [
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"-2*sqrt(3)/27 + 2/9 + I*(2*sqrt(3)/27 + 2/9)",
"2*sqrt(3)/27 + 2/9 + I*(-2/9 + 2*sqrt(3)/27)",
"2*sqrt(6)/27 + 2*sqrt(2)*I/9",
"2*sqrt(2)/9 - 2*sqrt(6)*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(6)/27 + 2*sqrt(2)*I/9",
"2*sqrt(2)/9 - 2*sqrt(6)*I/27",
"4*sqrt(3)/27 + 4*sqrt(3)*I/27",
"4*sqrt(3)/27 - 4*sqrt(3)*I/27",
"2*sqrt(2)/9 + 2*sqrt(6)*I/27",
"2*sqrt(2)/9 - 2*sqrt(6)*I/27",
"4*sqrt(3)/27 + 4*sqrt(3)*I/27",
"4*sqrt(3)/27 - 4*sqrt(3)*I/27",
"2*sqrt(2)/9 + 2*sqrt(6)*I/27",
"2*sqrt(6)/27 - 2*sqrt(2)*I/9",
"2*sqrt(3)/27 + 2/9 + I*(2/9 - 2*sqrt(3)/27)"
]
}
}