χ_R(∣qubit_H⟩^⊗1) ≤ 2

H-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

verified 2 stabilizer terms reproduce |qubit_H>^{ot 1}, checked symbolically

Implied per-copy exponent γ ≤ 1.0000 against a published 0.3962, no improvement.

Compute

1 run; 0.001 CPU-hours; 0.001 h wall-clock; on Apple silicon laptop, one core; direct construction, no search.

Notes

The single-copy cell. |qubit_H⟩ is not a stabilizer state (its nonzero amplitudes have two different moduli, the lower-bound certificate of the same cell), and it lies in the span of two stabilizer states; this is the first of the 12 rank-2 decompositions listed in research/constructions/data/qubit_H_m1_rank2.json, with coefficients fitted exactly. The implied exponent log_p(2) is the trivial one and moves nothing; the cell is filed so the orbit page shows χ = 2 at m = 1 as it does for S, T3, and T5.

Attribution

this repository · stabrank research/constructions/data · direct construction: the single-copy state as a combination of two stabilizer states

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "qubit_H",
  "m": 1,
  "direction": "upper",
  "rank": 2,
  "witness": {
    "terms": [
      {
        "k": 0,
        "x0": [
          0
        ],
        "W": [],
        "Q": [],
        "l": []
      },
      {
        "k": 1,
        "x0": [
          0
        ],
        "W": [
          [
            1
          ]
        ],
        "Q": [
          [
            0
          ]
        ],
        "l": [
          0
        ]
      }
    ],
    "coeffs": [
      "sqrt(1 - sqrt(2)/2)",
      "sqrt(1 - sqrt(2)/2)"
    ]
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank research/constructions/data",
    "method": "direct construction: the single-copy state as a combination of two stabilizer states",
    "date": "2026-10-17",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.001,
      "wall_clock_hours": 0.001,
      "runs": 1,
      "hardware": "Apple silicon laptop, one core; direct construction, no search"
    }
  },
  "notes": "The single-copy cell. |qubit_H> is not a stabilizer state (its nonzero amplitudes have two different moduli, the lower-bound certificate of the same cell), and it lies in the span of two stabilizer states; this is the first of the 12 rank-2 decompositions listed in research/constructions/data/qubit_H_m1_rank2.json, with coefficients fitted exactly. The implied exponent log_p(2) is the trivial one and moves nothing; the cell is filed so the orbit page shows chi = 2 at m = 1 as it does for S, T3, and T5."
}