A quantum low-density parity-check code. As in classical LDPC codes, the parity checks are sparse: each check involves only a few qubits and each qubit appears in only a few checks. It is a stabilizer code (here CSS), so it has two commuting sets of checks, X-type and Z-type. A code is summarized as [[n,k,d]]: n physical qubits encode k logical qubits, and the distance d is the lowest weight of an error that can go undetected.
Fault-tolerant quantum computing. The surface code works but spends a large number of physical qubits per logical qubit. qLDPC codes can encode more logical qubits at higher distance for the same number of physical qubits, while keeping the checks sparse and low-weight so syndrome extraction stays manageable. They are a leading route to lowering the qubit overhead of error correction.
To collect qLDPC codes in one place, with every entry's parameters checked automatically instead of taken on trust. The literature is scattered; this gathers codes, verifies them, and ranks them per track on a Pareto frontier, so it is easy to see this board's frontier and where there is room to do better. The frontier is board-relative: it reflects the codes seeded and submitted here, not an exhaustive snapshot of the literature.
The primary tracks are a computed grid of locality class by check-weight class. Within each cell, codes rank on a Pareto frontier over (n, k, d, w): a submission earns a record by beating that cell’s frontier with fewer physical qubits n, more logical qubits k, higher distance d, or lower check weight. Tighter cells nest into looser ones, so a strong 2D-local low-weight code also competes on the looser boards. The board holds the best we know of so you know what to aim past.
You do not pick them. The verifier computes each code’s locality class (single, bilayer, or unrestricted, derived from the layout) and its weight class (from the max check weight), so track membership cannot be gamed by relabeling. The construction family (bivariate bicycle, generalized bicycle, 2BGA, tile, and so on) is a separate self-declared tag, used only as a filter and never for ranking, because it cannot be recovered from the parity-check matrix.
The checks have to commute (the CSS condition) and stay sparse, which constrains the construction. You want high k, high d, and low n at the same time, and those pull against each other. Computing the distance d is NP-hard, so even measuring how good a candidate is can be expensive. Good codes tend to come from algebraic constructions (bicycle, product, lifted) whose parameters are hard to predict, so improving on them is largely search.
CI runs a verifier on every submission. It recomputes n and k over GF(2), checks the CSS commutation and the check weights, and confirms the distance witness is a genuine nontrivial logical operator of the claimed weight. That certifies the distance as an upper bound (d ≤) with no trust required. A code shows d= (certified exact) only when an independent certificate proves no shorter logical operator exists.
Distance d is the weight of the lightest nontrivial logical operator. There are two confidence levels. d≤ (upper bound) means a submission exhibits an explicit logical operator of that weight, found by a decoder-based search (BP+OSD random coset, or heuristics like QDistEvol); the verifier confirms it is a genuine logical, so the distance is at most that weight. The claim is also refutation-tested: independent searches (deep randomized information-set and BP+OSD passes at submission time, plus weekly fresh-seed sweeps of the whole board) try to find something lighter, which is evidence but not a proof. d= (certified exact) means a server-side integer program has proven no lighter logical exists. Exact certification is NP-hard and does not scale, so large codes carry a tight upper bound while small and moderate codes are certified exact. A d≤ record is provisional: if the true distance turns out lower, the entry is corrected.
It is an encoding-efficiency ratio: logical qubits times distance squared, per physical qubit. It comes from the Bravyi-Poulin-Terhal bound, which says a 2D-local code obeys kd² ≤ O(n), so under a locality or bounded-check-weight constraint kd²/n is bounded and measures how close a code gets to that ceiling (the surface code sits near 1). It is not a global record to chase: for high-rate codes with k and d both growing like n, kd²/n grows like n² without bound, so a large code trivially scores higher (the cited large-block codes reach the hundreds). So kd²/n is compared within a track, among codes of comparable size and check weight, not across the whole field. The headline number is the best among the codes on this board.
Bragging rights, chiefly. Your code lands on the board under your GitHub handle with a permanent link you can wave around, and if it advances a track's frontier it earns the record star (★). This is an open community leaderboard, so the rewards are accolades, a citable verified record, and the quiet respect of the few people who know what a good kd²/n means. No prize money, sorry.
Add one JSON file under codes/ following the schema and open a pull request; CI verifies it automatically. See CONTRIBUTING and the schema.