lean qubit_t_m3_stabRankP_le_three in LeanProofs.QubitTStabRank, machine-checked by Lean
Implied per-copy exponent γ ≤ 0.5283 against a published 0.3962, no improvement.
This bound is backed by a machine-checked theorem: qubit_t_m3_stabRankP_le_three in LeanProofs.QubitTStabRank. The recorded lake build confirms it compiles.
1 run; 0.01 CPU-hours; 0.01 h wall-clock; on Apple silicon laptop, 8 annealing chains.
Found here by the package's annealer (search_decomposition.py, target qubit_ttype, seed 1, one run of 8 chains) and verified in exact arithmetic with coefficients recovered by fit_coeffs. The phases need the fourth roots of unity, which the witness format now carries for qubits. Whether rank 2 is possible at m=3 is left open here.
this repository · stabrank annealer · simulated annealing over stabilizer states, then exact refit
{
"schema_version": "0.1",
"orbit": "qubit_T",
"m": 3,
"direction": "upper",
"rank": 3,
"witness": {
"terms": [
{
"k": 3,
"x0": [
0,
0,
0
],
"W": [
[
1,
0,
0
],
[
0,
1,
0
],
[
0,
0,
1
]
],
"Q": [
[
0,
1,
1
],
[
0,
0,
1
],
[
0,
0,
0
]
],
"l": [
3,
3,
0
]
},
{
"k": 2,
"x0": [
0,
0,
0
],
"W": [
[
1,
0,
0
],
[
0,
1,
0
]
],
"Q": [
[
0,
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],
[
0,
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]
],
"l": [
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]
},
{
"k": 2,
"x0": [
0,
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],
"W": [
[
1,
1,
0
],
[
0,
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1
]
],
"Q": [
[
0,
1
],
[
0,
0
]
],
"l": [
3,
0
]
}
],
"coeffs": [
"sqrt(2/3 - 2*sqrt(3)/9)",
"sqrt(sqrt(3)/6 + 1/2) - I*sqrt(sqrt(3)/18 + 1/6)",
"sqrt(1/2 - 5*sqrt(3)/18) + I*sqrt(sqrt(3)/18 + 1/6)"
]
},
"provenance": {
"author": "this repository",
"reference": "stabrank annealer",
"method": "simulated annealing over stabilizer states, then exact refit",
"date": "2026-09-16",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.01,
"wall_clock_hours": 0.01,
"runs": 1,
"hardware": "Apple silicon laptop, 8 annealing chains"
}
},
"notes": "Found here by the package's annealer (search_decomposition.py, target qubit_ttype, seed 1, one run of 8 chains) and verified in exact arithmetic with coefficients recovered by fit_coeffs. The phases need the fourth roots of unity, which the witness format now carries for qubits. Whether rank 2 is possible at m=3 is left open here.",
"lean": {
"module": "LeanProofs.QubitTStabRank",
"theorem": "qubit_t_m3_stabRankP_le_three"
}
}