χ_R(∣cat⟩^⊗8) ≥ 3

magic cat orbit, m qubits.

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.

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Verification

cited no runnable certificate; recorded as cited and cannot set a record

Notes

χ(cat_8) ≥ 3 by monotonicity from χ(cat_5) > 2 (Qassim, Pashayan, and Gosset, arXiv:2106.07740, appendix: ⟨0|_m |cat_m⟩ is proportional to |cat_{m-1}>, so χ(cat_m) ≥ χ(cat_{m-1}) for all m). Their Table 1 lists χ(cat_8) ≤ 6 and no lower bound beyond this. The board's attested χ(H^8) ≥ 6 gives the same 3 through χ(T^m)/2 ≤ χ(cat_m). Cited.

Attribution

Qassim, Pashayan, and Gosset · arXiv:2106.07740 · literature

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "cat",
  "m": 8,
  "direction": "lower",
  "rank": 3,
  "provenance": {
    "author": "Qassim, Pashayan, and Gosset",
    "reference": "arXiv:2106.07740",
    "date": "2021-06-14",
    "github": [],
    "method": "literature"
  },
  "notes": "chi(cat_8) >= 3 by monotonicity from chi(cat_5) > 2 (Qassim, Pashayan, and Gosset, arXiv:2106.07740, appendix: <0|_m |cat_m> is proportional to |cat_{m-1}>, so chi(cat_m) >= chi(cat_{m-1}) for all m). Their Table 1 lists chi(cat_8) <= 6 and no lower bound beyond this. The board's attested chi(H^8) >= 6 gives the same 3 through chi(T^m)/2 <= chi(cat_m). Cited."
}