Most efficient weight-6 qLDPC codes with exact distance
A quantum memory needs many logical qubits, each protected by a high distance, from as few physical qubits as possible. The efficiency k·d²/n measures that trade-off for codes whose checks hardware can measure with short circuits.
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 qldpcopen n144 example/n144.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 |
| qldpcopen.py | Validates submissions for this problem |
| qldpc.py | Distance search shared with qldpc |
How verification works
The verifier checks weights, degrees and commutation and computes k exactly over GF(2). It checks that the submitted operator has weight d, commutes with every check of the other type and is not a product of checks of its own type, so the distance is at most d. It then proves the distance is at least d with the exhaustive search of the qLDPC board, run for X and Z logical operators of weight up to d − 1 (each weight from 1 to the smaller of d − 1 and 10, then d − 1 once if it is larger; no search when d = 1): a minimum-weight logical operator contains no smaller nonzero codeword, so it is found by growing a support from each start qubit along unsatisfied checks, and a branch stops once its unsatisfied checks need more qubits than the remaining weight allows. If the search finds a lighter logical operator, the submission is rejected and the report includes it. The search must finish within 21,600 s of CPU time and 2³⁸ search nodes; otherwise the submission gets status error and is not ranked. A second checker, written separately, enumerates every codeword or every low-weight support of small codes and agreed with the verifier on all 201,321 test cases.