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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 files
Each JSON file defines one instance of this problem. Instances differ by check weight and ancilla limit. The verifier reads the same files, and the verifier bundle contains all of them together with an accepted example.
| File | Instance | Parameters | Size |
|---|---|---|---|
| z04-t2-a2.json | Weight 4, 2 ancillas | measure Z on 4 data qubits; two faults; at most 2 ancilla wires; debug instance | 0.3 KB |
| z06-t2-a3.json | Weight 6, 3 ancillas | measure Z on 6 data qubits; two faults; at most 3 ancilla wires; debug instance | 0.3 KB |
| z08-t2-a4.json | Weight 8, 4 ancillas | measure Z on 8 data qubits; two faults; at most 4 ancilla wires | 0.3 KB |
| z12-t2-a5.json | Weight 12, 5 ancillas | measure Z on 12 data qubits; two faults; at most 5 ancilla wires | 0.3 KB |
| z16-t2-a5.json | Weight 16, 5 ancillas | measure Z on 16 data qubits; two faults; at most 5 ancilla wires | 0.3 KB |