Stabilizer board

General (non-CSS) stabilizer codes, verified and ranked apart from the CSS board. Back to the CSS board.

7.624
[[85,8,9]] · w=6
best kd²/n at w ≤ 6
20.477
best kd²/n at w ≤ 8
26.145
[[235,96,8]] · w=10
best kd²/n at w ≤ 12
0.0053
[[108,12,6]] · r=7.0711 · ρ=1
best geometric efficiency
35.636
[[66,12,14]] · w=32
best kd²/n at any weight
135codes on the board
133submitted
2literature baselines

A general stabilizer code has one binary symplectic check matrix S = (A | B): generator i acts as X on Ai and Z on Bi, Y where both. A CSS code is the special case where every row is pure X or pure Z; here every code has at least one mixed generator (a code that is CSS up to a Hadamard on some qubits is filed as a duplicate of its CSS image, not listed twice). These codes are ranked on their own board because the quantities the CSS board reads per side have no side here:

CSS boardthis board
checksH_X, H_ZS = (A | B), isotropic: A Bᵀ + B Aᵀ = 0
kn − rank H_X − rank H_Zn − rank S
distanced = min(d_X, d_Z), one witness per sideone d: the minimum Pauli weight of a nontrivial logical operator (Y counts once); one Pauli-operator witness
check weight wrow weight|Ai ∪ Bi|
kd²/n, g, tracksunchanged; the primary-track cells are computed the same way, but carry the code type, so a record here is never a record there
certificateMILP per sidenot built yet: every entry stands as d ≤
circuit tiermemory circuits per basisnot accepted yet: syndrome extraction needs a general stabilizer-measurement schedule

Symplectic doubling maps any [[n, k, d]] stabilizer code to a CSS code [[2n, 2k, d′]] with d ≤ d′ ≤ 2d, so the two boards are linked; halving that map is how the highest-rate entries here were built. See the schema, tracks, and how to submit a stabilizer code (bring S, or A and B, as an .npz).

Leaderboard

4 contributors · 133 codes submitted through the challenge0 of 4 contributors have a verified layout and d ≥ 3 (their own code, or a layout they contributed)110 of 133 codes submitted through the challenge currently sit on a track frontier

weight ≤8
best kd²/n
35.636
[[66,12,14]] · d≤14 · w=32 · @MathysRennela
most codes on a frontier
82
82 of 102 codes · @FarLab

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/qldpc-challenge
cd qldpc-challenge
# bring your symplectic matrix S = (A | B) as mycode.npz (key s, or a and b)
./qldpc submit mycode.npz --authors @you

It finds the distance witness, runs the verifier, and opens the PR for you.

Have an LLM or coding agent? Paste the research prompt and it runs the whole loop. Full guide

Primary tracks

Computed grid of locality × check weight, derived from H and the layout, not self-declared. Each cell lists its Pareto frontier, ranked by the selected score (kd²/n, or geometric efficiency g for codes with a verified layout); codes tied on the score rank by the lowest (n, k) pair. The code count filters the table below to that cell. Membership nests: a tighter cell’s codes also compete in the looser ones. In the g view, the seeded surface/toric tilings are not raced; they set the ceiling g is normalized to (surface code = 1) and appear dimmed below the ranking.

Codes · 135 total, 111 records

weight4–8distance3–39n5–761k1–190

Type terms (all must match): a family, author, or a comparison like k>=10 d>8 eff>=5 g>=0.1 swaps<=50; ler<=0.005; record keeps only frontier rows and ler-record only the (n, k, LER) frontier; literature / submitted filter by origin; with-layout / no-layout filter by layout status; exact / upper-bound filter by whether the distance is proved; with-circuit (alias circuit) / no-circuit filter by whether the entry ships verified memory circuits; modular keeps the entries whose layout assigns every qubit to a module.

02004006000102030Code Distance (d)02004006000102030kd²/n
Physical Qubits (n)
Certified exactUpper boundFilled = Pareto recordOpen = non-frontier
★ record (shaded rows): Pareto-best on (n, k, d) within at least one computed cell, among the codes listed here. It is a board-relative marker, not a claim against the wider literature; a code the literature beats may still be seeded. certified exact (d =) upper bound (d ≤): a verified logical of that weight; independent refutation searches found nothing lighter, but it is not a proof submitted through the challenge (not a novelty claim; unmarked = literature baseline)known params parameter set exists in the literature; see provenance notesLER record Pareto-best on (n, k, measured logical error rate) among the codes with a measured rate; independent of the (n, k, d, w) record starcolumns: n physical qubits · k logical qubits · d distance (smallest undetectable error; the Pauli weight of the lightest logical operator, a Y factor counting one qubit) · kd²/n operational efficiency (per track) · g geometric efficiency 4kd²/(nρ²r⁴), priced by the layout’s radius r and layers ρ (surface code = 1; 2√2kd/(nρr³) for a 3D layout; · = no verified layout) · w max check weight (qubits a generator acts on, X, Z or Y) · swaps (optional) heuristic routing cost: nearest-neighbor SWAPs per round to connect every check on the verified layout, an MST lower bound with one lattice step = the minimum qubit spacing; a diagnostic, never a rank
codetypenkdkd²/ngwswapsgirthdiamauthorsmodeldate
★[[66,12,14]]other6612d ≤ 1435.636·32·4·@MathysRennelaMiMo v2.6 Flash2026-09-28
★[[62,20,10]]other6220d ≤ 1032.258·32·4·@MathysRennelaMiMo v2.6 Flash2026-09-28
★[[235,96,8]]pair-partition CPM23596d ≤ 826.145·10·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[329,190,6]]pair-partition CPM329190d ≤ 620.79·14·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[155,6,23]]other1556d ≤ 2320.477·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[355,144,7]]pair-partition CPM355144d ≤ 719.876·10·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[282,143,6]]pair-partition CPM282143d ≤ 618.255·12·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[144,10,16]]known paramsother14410d ≤ 1617.778·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[92,25,8]]known paramspair-partition CPM9225d ≤ 817.391·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
[[155,6,21]]other1556d ≤ 2117.071·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[96,10,12]]known paramsother9610d ≤ 1215.0·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[52,15,7]]known paramspair-partition CPM5215d ≤ 714.135·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[93,6,14]]other936d ≤ 1412.645·8·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[188,49,6]]pair-partition CPM18849d ≤ 69.383·8·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[75,7,10]]other757d ≤ 109.333·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[187,27,8]]other18727d ≤ 89.241·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[66,4,12]]other664d ≤ 128.727·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[99,17,7]]other9917d ≤ 78.414·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[40,9,6]]other409d ≤ 68.1·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[117,19,7]]other11719d ≤ 77.957·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[145,32,6]]pair-partition CPM14532d ≤ 67.945·10·4·@MathysRennelaMimo-V2.6-Flash2026-09-28
[[143,23,7]]other14323d ≤ 77.881·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[169,13,10]]other16913d ≤ 107.692·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[65,5,10]]other655d ≤ 107.692·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[50,6,8]]other506d ≤ 87.68·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[85,8,9]]known paramsother858d ≤ 97.624·6·4·@mrvee-qC-bee et al.GPT-6 Astra2026-10-01
★[[91,19,6]]other9119d ≤ 67.516·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[40,12,5]]other4012d ≤ 57.5·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[63,13,6]]other6313d ≤ 67.429·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[66,6,9]]other666d ≤ 97.364·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[105,21,6]]other10521d ≤ 67.2·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[171,25,7]]other17125d ≤ 77.164·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[48,7,7]]other487d ≤ 77.146·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[81,9,8]]other819d ≤ 87.111·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[45,5,8]]other455d ≤ 87.111·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[36,4,8]]other364d ≤ 87.111·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[91,13,7]]other9113d ≤ 77.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[77,11,7]]other7711d ≤ 77.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[63,9,7]]other639d ≤ 77.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[56,8,7]]other568d ≤ 77.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[36,7,6]]other367d ≤ 67.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[42,6,7]]other426d ≤ 77.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[35,5,7]]other355d ≤ 77.0·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[119,23,6]]other11923d ≤ 66.958·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[55,15,5]]other5515d ≤ 56.818·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[133,25,6]]other13325d ≤ 66.767·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[87,3,14]]other873d ≤ 146.759·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[65,17,5]]other6517d ≤ 56.538·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[32,4,7]]other324d ≤ 76.125·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[36,6,6]]other366d ≤ 66.0·6·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[105,25,5]]other10525d ≤ 55.952·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[51,3,10]]other513d ≤ 105.882·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[30,7,5]]other307d ≤ 55.833·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[143,13,8]]other14313d ≤ 85.818·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
[[121,11,8]]other12111d ≤ 85.818·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[33,3,8]]other333d ≤ 85.818·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[27,3,7]]other273d ≤ 75.444·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[12,4,4]]other124d ≤ 45.333·8·4·@MathysRennelaMiMo v2.6 Flash2026-09-28
★[[95,5,10]]other955d ≤ 105.263·6·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[38,2,10]]other382d ≤ 105.263·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[46,2,11]]other462d ≤ 115.261·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[189,27,6]]other18927d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[161,23,6]]other16123d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[147,21,6]]other14721d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[133,19,6]]other13319d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[119,17,6]]other11917d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[91,13,6]]other9113d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[77,11,6]]other7711d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[63,9,6]]other639d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[49,7,6]]other497d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[35,5,6]]other355d ≤ 65.143·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[28,4,6]]other284d ≤ 65.143·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[21,3,6]]other213d ≤ 65.143·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[25,5,5]]other255d ≤ 55.0·8·4·@davidpluGPT-62026-09-30
★[[20,4,5]]other204d ≤ 55.0·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[169,13,8]]other16913d ≤ 84.923·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
[[91,7,8]]other917d ≤ 84.923·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[65,5,8]]other655d ≤ 84.923·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[39,3,8]]other393d ≤ 84.923·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[26,2,8]]other262d ≤ 84.923·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[123,3,14]]other1233d ≤ 144.78·6·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[82,2,14]]other822d ≤ 144.78·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[34,2,9]]other342d ≤ 94.765·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[93,3,12]]other933d ≤ 124.645·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[62,2,12]]other622d ≤ 124.645·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[74,2,13]]other742d ≤ 134.568·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[142,2,18]]other1422d ≤ 184.563·6·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[188,95,3]]pair-partition CPM18895d ≤ 34.548·8·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[188,95,3]]pair-partition CPM18895d ≤ 34.548·8·4·@MathysRennelaSpace Bunny Alpha 1.02026-10-01
★[[178,2,20]]other1782d ≤ 204.494·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[69,3,10]]other693d ≤ 104.348·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[46,2,10]]other462d ≤ 104.348·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[177,3,16]]other1773d ≤ 164.339·6·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[134,2,17]]other1342d ≤ 174.313·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[57,3,9]]other573d ≤ 94.263·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[58,2,11]]other582d ≤ 114.172·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
[[94,2,14]]other942d ≤ 144.17·6·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[18,3,5]]other183d ≤ 54.167·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[11,5,3]]other115d ≤ 34.091·8·4·@MathysRennelaMiMo v2.6 Flash2026-09-28
★[[256,16,8]]known paramstopological25616d ≤ 84.00.0015676847.07Chamon, ClaudioClaudeClaude Fable 5.12005
[[108,12,6]]known paramstopological10812d ≤ 64.00.0053621645.1Chamon, ClaudioClaudeClaude Fable 5.12005
★[[155,5,11]]other1555d ≤ 113.903·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
[[111,3,12]]other1113d ≤ 123.892·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[33,2,8]]other332d ≤ 83.879·7·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[28,3,6]]other283d ≤ 63.857·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[20,3,5]]other203d ≤ 53.75·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[20,2,6]]other202d ≤ 63.6·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[8,3,3]]other83d ≤ 33.375·6·4·@MathysRennelaMiMo v2.6 Flash2026-09-28
★[[38,2,8]]other382d ≤ 83.368·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[75,10,5]]other7510d ≤ 53.333·7·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[10,2,4]]other102d ≤ 43.2·6·4·@MathysRennelaMiMo v2.6 Flash2026-09-28
★[[53,1,13]]other531d ≤ 133.189·8·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[173,1,23]]other1731d ≤ 233.058·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[151,1,21]]other1511d ≤ 212.921·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[34,2,7]]other342d ≤ 72.882·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[17,1,7]]known paramsother171d ≤ 72.882·8·4·@FarLabClaudeClaude Fable 5.12026-09-30
★[[127,1,19]]other1271d ≤ 192.843·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[29,1,9]]other291d ≤ 92.793·8·4·@davidpluGPT-62026-09-30
[[27,3,5]]other273d ≤ 52.778·6·4·@davidpluGPT-62026-09-30
★[[18,2,5]]other182d ≤ 52.778·5·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[27,2,6]]other272d ≤ 62.667·5·4·@FarLabClaudeClaude Fable 5.12026-10-01
[[137,1,19]]other1371d ≤ 192.635·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[31,1,9]]other311d ≤ 92.613·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[113,1,17]]other1131d ≤ 172.558·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[89,1,15]]other891d ≤ 152.528·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[39,2,7]]other392d ≤ 72.513·5·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[21,1,7]]other211d ≤ 72.333·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
[[23,1,7]]other231d ≤ 72.13·6·4·@davidpluGPT-62026-09-30
★[[18,1,6]]other181d ≤ 62.0·6·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[761,1,39]]known paramstopological7611d ≤ 391.999·4·4·@mrvee-qC-beeGPT-6 Astra2026-10-01
★[[25,1,7]]other251d ≤ 71.96·4·4·@FarLabClaudeClaude Fable 5.12026-10-01
★[[14,3,3]]topological143d ≤ 31.929·4·4·@MathysRennelaMimo-V2.6-Flash2026-09-27
★[[13,1,5]]topological131d ≤ 51.923·4·4·@MathysRennelaMimo-V2.6-Flash2026-09-27
★[[25,5,3]]other255d ≤ 31.8·6·4·@davidpluGPT-62026-09-30
★[[5,1,3]]other51d ≤ 31.8·4·4·@MathysRennelaMimo-V2.6-Flash2026-09-27

Recently added · last 10 by submission date

  1. [[96,10,12]]★other@mrvee-qC-beesubmission2026-10-01
  2. [[93,6,14]]★other@mrvee-qC-beesubmission2026-10-01
  3. [[93,3,12]]★other@FarLabsubmission2026-10-01
  4. [[92,25,8]]★pair-partition CPM@mrvee-qC-beesubmission2026-10-01
  5. [[91,7,8]]other@FarLabsubmission2026-10-01
  6. [[91,13,6]]★other@FarLabsubmission2026-10-01
  7. [[89,1,15]]★other@FarLabsubmission2026-10-01
  8. [[85,8,9]]★other@mrvee-qC-bee et al.submission2026-10-01
  9. [[82,2,14]]★other@FarLabsubmission2026-10-01
  10. [[77,11,6]]★other@FarLabsubmission2026-10-01