χR(∣qubit_H⟩⊗6) ≥ 4

H-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_H^6) >= 4

Compute

1 run; 0.3 CPU-hours; 0.08 h wall-clock; on Apple silicon laptop, 8 worker processes.

Notes

Projection monotonicity from m=4, with the m=4 rank-3 exclusion re-run inside the certificate rather than taken from the board: χ(ψ ⊗ φ) ≥ χ(ψ) whenever φ has a nonzero computational amplitude, since applying I ⊗ ⟨x| to a decomposition of ψ ⊗ φ maps each stabilizer state to a stabilizer state or zero (the lemma is written out in the certificate). Leaves the cell at 4 ≤ χ ≤ 6.

Attribution

Labib and Russo · arXiv:2605.28586 · literature

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "qubit_H",
  "m": 6,
  "direction": "lower",
  "rank": 4,
  "provenance": {
    "author": "Labib and Russo",
    "reference": "arXiv:2605.28586",
    "method": "literature",
    "date": "2026-05-27",
    "github": [
      "FarLab",
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.3,
      "wall_clock_hours": 0.08,
      "runs": 1,
      "hardware": "Apple silicon laptop, 8 worker processes"
    }
  },
  "notes": "Projection monotonicity from m=4, with the m=4 rank-3 exclusion re-run inside the certificate rather than taken from the board: chi(psi (x) phi) >= chi(psi) whenever phi has a nonzero computational amplitude, since applying I (x) <x| to a decomposition of psi (x) phi maps each stabilizer state to a stabilizer state or zero (the lemma is written out in the certificate). Leaves the cell at 4 <= chi <= 6.",
  "certificate": {
    "script": "verify_challenge/cert_qubit_h_m6_from_m4.py",
    "expect": "CERTIFIED chi(qubit_H^6) >= 4"
  }
}