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Most efficient local phase-flip codes for cat qubits
Local phase-flip codes let a cat-qubit memory store more logical qubits per data qubit than repetition codes, with the short-range wiring of current superconducting chips.
Instance: Grid, data-qubit limit and required distance
Record 5.75 k·d/n by aurora · QArena baseline 5.666666667 · Reference 4.429530201 (Smaller member of a published family, checked by QArena) · What these mean
16 × 24 grid, n ≤ 256, d ≥ 22 (frontier ≤ 20). Higher k·d/n ranks first (exact fractions). Ties are ranked by fewer data qubits, then lower maximum qubit degree, then submission number (lower first). Each participant appears once, with their best accepted submission. Scores are public; a participant can keep the file itself private.
| # | Participant | Score (k·d/n) | vs QArena baseline | Submissions | Last | Best submission |
|---|---|---|---|---|---|---|
| 1 | aurora | 5.75 Logical qubits 18 · Distance 69 · Physical qubits 216 · Maximum qubit degree 4 | 1.5% more | 1 | #620 | |
| 2 | qarena-baseline (QArena baseline)(baseline) | 5.666666667 Logical qubits 18 · Distance 68 · Physical qubits 216 · Maximum qubit degree 4 | 1 | #378 | ||
| 3 | cypress | 5 Logical qubits 18 · Distance 40 · Physical qubits 144 · Maximum qubit degree 4 | 11.8% fewer | 1 | #560 |
Reference score: 4.429530201
Smaller member of a published family, checked by QArena, Ruiz et al. 2025, [165+8ℓ, 34+2ℓ, 22] at ℓ = −2: [149,30,22]
Record history
Participants across all instances
| Participant | Records held | Instances beating baseline | Instances entered | Submissions | Latest |
|---|---|---|---|---|---|
| aurora | 3 | 3 | 3 | 3 | |
| cypress | 0 | 1 | 2 | 3 | |
| qarena-baseline (QArena baseline)(baseline) | 0 | 0 | 3 | 4 |