χR(∣qubit_sqrtT⟩⊗6) ≥ 6

√T 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

verified   certificate script asserted: CERTIFIED chi(qubit_sqrtT^6) >= 6, by an argument declared exact throughout (no floating-point margin)

Compute

3 runs; 0.02 CPU-hours; 0.01 h wall-clock; on Apple silicon laptop (shared, load 70), three census runs of 25 s each at m = 4 and 5; claude-fable-5-1, found the forced-subspace reduction, wrote the census and the certificate.

Notes

(⟨0| ⊗ I)|sqrtT⟩⊗6 = 2^{-1/2} |sqrtT⟩⊗5 and a computational-basis slice of a stabilizer state is a stabilizer state or zero, so χ(|sqrtT⟩⊗6) ≥ χ(|sqrtT⟩⊗5) = 6 (qubit_sqrtT-m5-lower-6.json, exact). First lower bound for this cell; with the product upper bound 12 the cell is 6 ≤ χ ≤ 12, and χ ≤ 7 here would beat the published exponent 1/2 (log_2(7)/6 = 0.4680). The six product states φ^6 span only the hyperplane f(1) = f(5) of Sym^6 and no symmetric six-qubit stabilizer state leaves it, so the symmetric construction that gives the m ≤ 5 witnesses stops at m = 6.

Attribution

Vincent Russo · this repository (stabrank-research, round 33) · projection monotonicity applied to the exact rank-5 exclusion at m=5

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "qubit_sqrtT",
  "m": 6,
  "direction": "lower",
  "rank": 6,
  "certificate": {
    "script": "verify_challenge/cert_sqrtt_galois_census.py",
    "expect": "CERTIFIED chi(qubit_sqrtT^6) >= 6",
    "exact": true
  },
  "provenance": {
    "author": "Vincent Russo",
    "reference": "this repository (stabrank-research, round 33)",
    "method": "projection monotonicity applied to the exact rank-5 exclusion at m=5",
    "date": "2026-10-23",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.02,
      "wall_clock_hours": 0.01,
      "runs": 3,
      "hardware": "Apple silicon laptop (shared, load 70), three census runs of 25 s each at m = 4 and 5",
      "llm": [
        {
          "model": "claude-fable-5-1",
          "role": "found the forced-subspace reduction, wrote the census and the certificate"
        }
      ]
    }
  },
  "notes": "(<0| (x) I)|sqrtT>^6 = 2^{-1/2} |sqrtT>^5 and a computational-basis slice of a stabilizer state is a stabilizer state or zero, so chi(|sqrtT>^6) >= chi(|sqrtT>^5) = 6 (qubit_sqrtT-m5-lower-6.json, exact). First lower bound for this cell; with the product upper bound 12 the cell is 6 <= chi <= 12, and chi <= 7 here would beat the published exponent 1/2 (log_2(7)/6 = 0.4680). The six product states phi^6 span only the hyperplane f(1) = f(5) of Sym^6 and no symmetric six-qubit stabilizer state leaves it, so the symmetric construction that gives the m <= 5 witnesses stops at m = 6."
}