verified 16 stabilizer terms reproduce |S>^{ot 7}, checked symbolically
Implied per-copy exponent γ ≤ 0.3605 against a published 0.3155, 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 S-m4-upper-4.json, S-m2-upper-2.json, S-m1-upper-2.json: χ(|S⟩⊗4) ≤ 4 x χ(|S⟩⊗2) ≤ 2 x χ(|S⟩⊗1) ≤ 2 gives χ(|S⟩⊗7) ≤ 16, exponent 0.3605. 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": "S",
"m": 7,
"direction": "upper",
"rank": 16,
"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 S-m4-upper-4.json, S-m2-upper-2.json, S-m1-upper-2.json: chi(|S>^4) <= 4 x chi(|S>^2) <= 2 x chi(|S>^1) <= 2 gives chi(|S>^7) <= 16, exponent 0.3605. 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": [
"3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"3*sqrt(6)*I/16",
"3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"3*sqrt(6)*I/16",
"3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"-3*sqrt(6)*I/16",
"3*sqrt(6)*I/16"
]
}
}