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.
Verifier
The verifier checks your file and computes its score. The server runs the same code on every submission.
Download the bundle, extract it and run these commands from its folder (the one holding verifiers/). The bundle
includes an accepted example file.
python3 -m pip install -r requirements.txt python3 -I verifiers/run_one.py flagcheck z12-t2-a5 example/z12-t2-a5.json
The verifier prints one line of JSON with a status: accepted with the score, rejected with the reason,
or error if verification could not finish.
Files
| File | Role |
|---|---|
| run_one.py | Runs the verifier |
| common.py | Shared helpers |
| flagcheck.py | Validates submissions for this problem |
How verification works
The verifier runs the circuit once on w Bell pairs, each made of a data qubit and an untouched reference qubit, with an exact stabilizer simulation in which every sign is a parity of random measurement outcomes, so one run covers every outcome. Every flag must be 0, the syndrome must be a fair coin, and the final state must be exactly the Bell pairs projected onto the measured parity. That holds exactly when the circuit performs the ideal parity measurement. Then each possible fault (one of 15 two-qubit Paulis after a CNOT, a flipped preparation, a flipped outcome) is pushed to the end of the circuit as a Pauli frame, and every single fault and every pair of faults at different operations is checked: if no flag fires, the data error E must satisfy min(wt(E), wt(E·Z⊗w)) ≤ the number of faults. A second, independently written program re-simulates every fault event with a full stabilizer tableau; it agreed with the verifier on 8,160 test artifacts, including the exact number of undetected fault events.