verified 9 stabilizer terms reproduce |qubit_T>^{ot 8}, checked symbolically
Implied per-copy exponent γ ≤ 0.3962 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: χ(|qubitT⟩⊗4) ≤ 3 x χ(|qubitT⟩⊗4) ≤ 3 gives χ(|qubitT⟩⊗8) ≤ 9, exponent 0.3962. 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": 8,
"direction": "upper",
"rank": 9,
"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: chi(|qubit_T>^4) <= 3 x chi(|qubit_T>^4) <= 3 gives chi(|qubit_T>^8) <= 9, exponent 0.3962. 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.",
"witness": {
"terms": [
{
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[
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[
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"Q": [
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[
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[
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[
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[
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"l": [
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{
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{
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"Q": [
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[
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"l": [
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]
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{
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],
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[
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[
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"Q": [
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[
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{
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],
"W": [
[
1,
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[
0,
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[
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[
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"Q": [
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0,
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[
0,
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[
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{
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[
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]
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{
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],
"W": [
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1,
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[
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"Q": [
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"l": [
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{
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"W": [
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1,
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[
0,
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[
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"Q": [
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{
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],
"W": [
[
1,
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"Q": [
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[
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[
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],
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]
}
],
"coeffs": [
"2*sqrt(3)/9 + 2*I/9",
"(2*sqrt(sqrt(3) + 2) + 2*I*sqrt(2 - sqrt(3)))/9",
"4/9",
"(2*sqrt(sqrt(3) + 2) + 2*I*sqrt(2 - sqrt(3)))/9",
"4/9",
"(2*sqrt(sqrt(3) + 2) - 2*I*sqrt(2 - sqrt(3)))/9",
"4/9",
"(2*sqrt(sqrt(3) + 2) - 2*I*sqrt(2 - sqrt(3)))/9",
"2*sqrt(3)/9 - 2*I/9"
]
}
}