χ_R(∣qubit_T⟩^⊗2) ≥ 2

BK T-type orbit, qubit.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

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Verification

lean qubit_t_m2_stabRankP_gt_one in LeanProofs.QubitM2Lower, machine-checked by Lean

Lean proof

This bound is backed by a machine-checked theorem: qubit_t_m2_stabRankP_gt_one in LeanProofs.QubitM2Lower. The recorded lake build confirms it compiles.

Notes

Settles χ(T^2) = 2 with the Lean upper bound qubit_t_m2_stabRankP_le_two. |T⟩^⊗2 has moduli cos^2(β) and cos(β) sin(β) with β = arccos(1/√3)/2, which differ. Also proved in Lean against stabRankP 2: QubitM2Lower.qubit_t_m2_stabRankP_gt_one (equal fourth powers at 00 and 01 would force √3 = -2).

Attribution

this repository · stabrank verify_challenge · exact: the state is not a stabilizer state (two distinct amplitude moduli)

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "qubit_T",
  "m": 2,
  "direction": "lower",
  "rank": 2,
  "certificate": {
    "script": "verify_challenge/cert_rank1_moduli.py",
    "expect": "CERTIFIED chi(qubit_T^2) >= 2",
    "exact": true
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank verify_challenge",
    "method": "exact: the state is not a stabilizer state (two distinct amplitude moduli)",
    "date": "2026-09-20",
    "github": [
      "vprusso"
    ]
  },
  "notes": "Settles chi(T^2) = 2 with the Lean upper bound qubit_t_m2_stabRankP_le_two. |T>^2 has moduli cos^2(beta) and cos(beta) sin(beta) with beta = arccos(1/sqrt3)/2, which differ. Also proved in Lean against stabRankP 2: QubitM2Lower.qubit_t_m2_stabRankP_gt_one (equal fourth powers at 00 and 01 would force sqrt3 = -2).",
  "lean": {
    "module": "LeanProofs.QubitM2Lower",
    "theorem": "qubit_t_m2_stabRankP_gt_one"
  }
}