χ_R(∣cat⟩^⊗2) ≤ 1

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

verified 1 stabilizer terms reproduce |cat_2>, checked symbolically

Notes

χ(|cat₂⟩) = 1: |cat₂⟩ = 2^{-1/2}(|00⟩ + i|11⟩) is a stabilizer state (Qassim, Pashayan, and Gosset, Eq. 5 and Table 1). The one-term witness is the state itself. The m = 2 cell implies no exponent, since the gluing identity has denominator m - 2.

Attribution

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

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "cat",
  "m": 2,
  "direction": "upper",
  "rank": 1,
  "provenance": {
    "author": "Qassim, Pashayan, and Gosset",
    "reference": "arXiv:2106.07740",
    "method": "literature",
    "date": "2021-06-14",
    "github": []
  },
  "notes": "chi(|cat_2>) = 1: |cat_2> = 2^{-1/2}(|00> + i|11>) is a stabilizer state (Qassim, Pashayan, and Gosset, Eq. 5 and Table 1). The one-term witness is the state itself. The m = 2 cell implies no exponent, since the gluing identity has denominator m - 2.",
  "witness": {
    "terms": [
      {
        "k": 1,
        "x0": [
          0,
          0
        ],
        "W": [
          [
            1,
            1
          ]
        ],
        "Q": [
          [
            0
          ]
        ],
        "l": [
          1
        ]
      }
    ],
    "coeffs": [
      "1"
    ]
  }
}