χ_R(∣qubit_T⟩^⊗5) ≥ 4

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^5) >= 4

Compute

1 run; 0.01 CPU-hours; 0.005 h wall-clock; on Apple silicon laptop.

Notes

A rank-3 decomposition of |T⟩^⊗5 sliced along one qubit gives a rank-3 decomposition of |T⟩^⊗4 whose terms are related slice to slice by a Pauli and a fourth root of unity. |T⟩^⊗4 has one rank-3 decomposition up to its unitary symmetries (the QubitTM4 witness), and no choice of Paulis and phases satisfies the second slice, so rank 3 is impossible at m=5. Puts the cell at 4 ≤ χ ≤ 6.

Attribution

this repository · stabrank slice_lift.py · slice-and-lift: every rank-3 decomposition of |T⟩^⊗4 up to symmetry, none extends to |T⟩^⊗5

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "qubit_T",
  "m": 5,
  "direction": "lower",
  "rank": 4,
  "certificate": {
    "script": "verify_challenge/cert_qubit_t_m5_lift.py",
    "expect": "CERTIFIED chi(qubit_T^5) >= 4"
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank slice_lift.py",
    "method": "slice-and-lift: every rank-3 decomposition of |T>^4 up to symmetry, none extends to |T>^5",
    "date": "2026-09-18",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.01,
      "wall_clock_hours": 0.005,
      "runs": 1,
      "hardware": "Apple silicon laptop"
    }
  },
  "notes": "A rank-3 decomposition of |T>^5 sliced along one qubit gives a rank-3 decomposition of |T>^4 whose terms are related slice to slice by a Pauli and a fourth root of unity. |T>^4 has one rank-3 decomposition up to its unitary symmetries (the QubitTM4 witness), and no choice of Paulis and phases satisfies the second slice, so rank 3 is impossible at m=5. Puts the cell at 4 <= chi <= 6."
}