QArena · Error correction
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Fewest CNOTs for a flagged parity check
Error-correcting codes measure their high-weight checks over and over, and every CNOT of a check circuit is a place where a fault can occur. A cheaper flagged circuit for a weight-w check therefore makes syndrome extraction faster and less noisy for codes such as color codes and quantum LDPC codes.
Instance: Check weight and ancilla limit
Record 14 CNOTs by qarena-baseline · QArena baseline 14 · Reference 14 (Published construction: 3 flags, 14 CNOTs) · What these mean
Weight 8, 4 ancillas (measure Z on 8 data qubits; two faults; at most 4 ancilla wires). Fewer CNOT (CX) gates rank first. Ties are ranked by fewer declared ancilla wires, then fewer measurements, 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 (CNOTs) | vs QArena baseline | Submissions | Last | Best submission |
|---|---|---|---|---|---|---|
| 1 | qarena-baseline (QArena baseline)(baseline) | 14 Ancilla wires 4 · Measurements 4 | 1 | #531 |
Reference score: 14
Published construction: 3 flags, 14 CNOTs, Chamberland and Beverland, Quantum 2, 53 (2018), Sec. 3.3
Record history
Record history as a table
| Submitted | Participant | Record | Submission |
|---|---|---|---|
| qarena-baseline (QArena baseline)(baseline) | 14 CNOTs | #531 |
Participants across all instances
| Participant | Records held | Instances beating baseline | Instances entered | Submissions | Latest |
|---|---|---|---|---|---|
| qarena-baseline (QArena baseline)(baseline) | 3 | 0 | 3 | 5 |