χR(∣qubit_sqrtT⟩⊗7) ≤ 12

√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   12 stabilizer terms reproduce |qubit_sqrtT>^{ot 7}, checked symbolically

Implied per-copy exponent γ ≤ 0.5121 against a published 0.5000, no improvement.

Compute

37 runs; 22.7452 CPU-hours; 8.5804 h wall-clock; on x86_64 Linux, 256 cores; claude-fable-5-1, drove the search.

Notes

Found by autoresearch/run.py on seed 312002 after 0 failed seed(s) at this rank (residuals none). Implied γ 0.5121. Every run is logged in autoresearch/runs.jsonl. Lower bound at m = 7 is 7 by projection from m = 6. Product bound at m = 7 is 24.

Attribution

Vincent Russo · stabrank autoresearch/run.py on Perlmutter (round 33 of stabrank-research, job 60161156) · simulated annealing at rank 12 (8 chains, 8000 iterations per temperature, cooling 0.995), then exact refit

Submission

JSON
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  "orbit": "qubit_sqrtT",
  "m": 7,
  "direction": "upper",
  "rank": 12,
  "witness": {
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    ],
    "coeffs": [
      "-exp(5*I*pi/8)/8 - exp(I*pi/4)/8 + exp(I*pi/8)/8 + exp(3*I*pi/4)/8",
      "-exp(5*I*pi/8)/8 - exp(3*I*pi/4)/8 + exp(I*pi/8)/8 + exp(I*pi/4)/8",
      "-exp(5*I*pi/8)/8 - exp(3*I*pi/4)/8 + exp(I*pi/8)/8 + exp(I*pi/4)/8",
      "-3*exp(I*pi/4)/8 - exp(5*I*pi/8)/8 - exp(3*I*pi/4)/8 + exp(I*pi/8)/8 + I/2",
      "-exp(3*I*pi/8)/4 - exp(5*I*pi/8)/8 - exp(I*pi/8)/8 + exp(3*I*pi/4)/8 + exp(I*pi/4)/8 + I/4",
      "-sqrt(2)*I/4 - sqrt(2)*exp(3*I*pi/8)/4 + sqrt(2)*exp(I*pi/4)/4 + sqrt(2)*exp(5*I*pi/8)/4",
      "1/16 - I/16 - exp(I*pi/4)/16 - exp(3*I*pi/4)/16 - exp(I*pi/8)/16 + exp(7*I*pi/8)/16 + exp(5*I*pi/8)/16 + exp(3*I*pi/8)/16",
      "-exp(5*I*pi/8)/8 - exp(3*I*pi/4)/8 + exp(I*pi/8)/8 + exp(I*pi/4)/8",
      "exp(I*pi/8)/8 + exp(3*I*pi/4)/8 + exp(I*pi/4)/8 + exp(5*I*pi/8)/8 + exp(3*I*pi/8)/4 + I/4",
      "-exp(5*I*pi/8)/8 - exp(I*pi/4)/8 + exp(I*pi/8)/8 + exp(3*I*pi/4)/8",
      "-exp(5*I*pi/8)/8 - exp(I*pi/4)/8 + exp(I*pi/8)/8 + exp(3*I*pi/4)/8",
      "1/16 - I/16 - exp(3*I*pi/8)/16 - exp(I*pi/8)/16 - exp(7*I*pi/8)/16 + exp(3*I*pi/4)/16 + exp(I*pi/4)/16 + exp(5*I*pi/8)/16"
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  },
  "provenance": {
    "author": "Vincent Russo",
    "reference": "stabrank autoresearch/run.py on Perlmutter (round 33 of stabrank-research, job 60161156)",
    "method": "simulated annealing at rank 12 (8 chains, 8000 iterations per temperature, cooling 0.995), then exact refit",
    "date": "2026-10-23",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 22.7452,
      "wall_clock_hours": 8.5804,
      "runs": 37,
      "hardware": "x86_64 Linux, 256 cores",
      "llm": [
        {
          "model": "claude-fable-5-1",
          "role": "drove the search"
        }
      ]
    }
  },
  "notes": "Found by autoresearch/run.py on seed 312002 after 0 failed seed(s) at this rank (residuals none). Implied gamma 0.5121. Every run is logged in autoresearch/runs.jsonl. Lower bound at m = 7 is 7 by projection from m = 6. Product bound at m = 7 is 24."
}