χ_R(∣qubit_T⟩^⊗3) ≥ 3

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.

← back to the board

Verification

reproduced certificate script asserted: CERTIFIED chi(qubit_T^3) >= 3

Compute

1 run; 0.001 CPU-hours; 0.001 h wall-clock; on Apple silicon laptop.

Notes

Pairs with the annealed rank-3 decomposition to settle χ(|T⟩^⊗3) = 3 exactly. The exclusion is numerical and rests on a margin: the closest any two key-adjacent quotient directions come to parallel is 0.81 against a threshold of 1 - 1e-6. The T-type state at m=2, whose rank-2 decomposition is verified on the board, is the positive control.

Attribution

this repository · stabrank rank_exclusion.py · exhaustion over all pairs of 3-qubit stabilizer states, via the quotient by the target

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "qubit_T",
  "m": 3,
  "direction": "lower",
  "rank": 3,
  "certificate": {
    "script": "verify_challenge/cert_qubit_t_m3_rank2.py",
    "expect": "CERTIFIED chi(qubit_T^3) >= 3"
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank rank_exclusion.py",
    "method": "exhaustion over all pairs of 3-qubit stabilizer states, via the quotient by the target",
    "date": "2026-09-16",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.001,
      "wall_clock_hours": 0.001,
      "runs": 1,
      "hardware": "Apple silicon laptop"
    }
  },
  "notes": "Pairs with the annealed rank-3 decomposition to settle chi(|T>^3) = 3 exactly. The exclusion is numerical and rests on a margin: the closest any two key-adjacent quotient directions come to parallel is 0.81 against a threshold of 1 - 1e-6. The T-type state at m=2, whose rank-2 decomposition is verified on the board, is the positive control."
}