QEC Challenge

147

submitted codes

literature baselines

534.324

[[482,146,42]] · w=28

best operational efficiency

[[25,1,5]] · r=1.4142 · ρ=1

best geometric efficiency

Operational efficiencykd²/n

The Bravyi–Poulin–Terhal ratio, normalized so the surface code sits at 1. Bounded for 2D-local and bounded-weight codes; grows with n for high-rate codes, so it is compared within tracks, not as a global record.

Geometric efficiencyg = 4kd²/(nρ²r⁴)

The same ratio priced by the layout the code ships with, normalized so the planar surface code scores exactly 1. Computed only for codes with a verifier-accepted layout; an upper-bound distance makes g an upper bound, and the headline requires d ≥ 3.

n physical qubits · k logical qubits · d code distance (smallest undetectable error) · w max check weight · r interaction radius: the largest check diameter in the layout, in units of the minimum qubit spacing · ρ qubit layers per site (2 = flip-chip bilayer; charged as ρ² so stacking must earn its density)

Record progress

w ≤ 6w ≤ 8any w○ new record

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). 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.

	weight ≤ 4	weight ≤ 6	weight ≤ 8	any weight
2D-local single	d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[16,2,4]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d =[[18,4,4]]3.556 d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d =[[16,6,4]]6 d =[[15,7,3]]4.2 d =[[18,4,4]]3.556 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d =[[16,6,4]]6 d =[[15,7,3]]4.2 d =[[18,4,4]]3.556 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533
2D-local bilayer	d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[16,2,4]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d =[[72,12,6]]6 d =[[62,10,6]]5.806 d =[[48,4,8]]5.333 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d ≤[[384,12,17]]9.031 d ≤[[263,16,12]]8.76 d =[[216,15,11]]8.403 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d ≤[[384,12,17]]9.031 d ≤[[263,16,12]]8.76 d =[[216,15,11]]8.403 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533
unrestricted	d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[16,2,4]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d ≤[[360,12,24]]19.2 d ≤[[340,16,18]]15.247 d ≤[[288,16,16]]14.222 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d ≤[[684,8,85]]84.503 d ≤[[584,150,18]]83.219 d ≤[[472,122,14]]50.661 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533	d ≤[[482,146,42]]534.324 d ≤[[390,82,38]]303.61 d ≤[[390,82,32]]215.303 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

weight ≤ 4

weight ≤ 6

weight ≤ 8

any weight

2D-local single

d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[16,2,4]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d =[[18,4,4]]3.556 d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d =[[16,6,4]]6 d =[[15,7,3]]4.2 d =[[18,4,4]]3.556 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

2D-local bilayer

d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[16,2,4]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d =[[72,12,6]]6 d =[[62,10,6]]5.806 d =[[48,4,8]]5.333 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d ≤[[384,12,17]]9.031 d ≤[[263,16,12]]8.76 d =[[216,15,11]]8.403 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

unrestricted

d =[[64,2,8]]2 d =[[36,2,6]]2 d =[[16,2,4]]2 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d ≤[[360,12,24]]19.2 d ≤[[340,16,18]]15.247 d ≤[[288,16,16]]14.222 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d ≤[[684,8,85]]84.503 d ≤[[584,150,18]]83.219 d ≤[[472,122,14]]50.661 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

d ≤[[482,146,42]]534.324 d ≤[[390,82,38]]303.61 d ≤[[390,82,32]]215.303 d =[[625,50,3]]0.72 d ≤[[361,26,3]]0.648 d ≤[[169,10,3]]0.533

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Recently added · last 10 by submission date

[[684,10,101]]★2BGA coset@vprussosubmission2026-08-09
[[384,12,17]]★bivariate bicycle@mathysrennelasubmission2026-08-09
[[361,26,3]]★topological@mathysrennelasubmission2026-08-09
[[169,10,3]]★topological@mathysrennelasubmission2026-08-09
[[625,50,3]]★topological@aarontrowbridgesubmission2026-08-07
[[592,8,32]]★lifted product@vprussosubmission2026-08-07
[[576,8,32]]★lifted product@vprussosubmission2026-08-07
[[482,146,42]]★generalized bicycle@yhu1996submission2026-08-07
[[376,6,32]]★lifted product@vprussosubmission2026-08-07
[[348,4,34]]★lifted product@vprussosubmission2026-08-07

Codes · 231 total, 194 records

weight4–32distance2–101n7–700k1–292

Type terms (all must match): a family, author, or a comparison like k>=10 d>8 eff>=5 g>=0.1; record keeps only frontier rows; literature / submitted filter by origin; with-layout / no-layout filter by layout status.

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 notescolumns: n physical qubits · k logical qubits · d distance (smallest undetectable error) · kd²/n operational efficiency (per track) · g geometric efficiency 4kd²/(nρ²r⁴), priced by the layout’s radius r and layers ρ (surface code = 1; · = no verified layout) · w max check weight

	code	type	n	k	d	kd²/n	g	w	authors	model	date
★	[[482,146,42]]	generalized bicycle	482	146	d ≤ 42	534.324	·	28	@yhu1996	Claude Opus 5	2026-08-07
★	[[390,82,38]]	generalized bicycle	390	82	d ≤ 38	303.61	·	32	@mathysrennela and @seunomonije	Tencent Hy3	2026-07-19
★	[[390,82,32]]	generalized bicycle	390	82	d ≤ 32	215.303	·	16	@seunomonije	Claude Fable 5	2026-07-18
	[[390,82,31]]	generalized bicycle	390	82	d ≤ 31	202.056	·	16	@seunomonije	Claude Fable 5	2026-07-18
	[[390,82,30]]	generalized bicycle	390	82	d ≤ 30	189.231	·	16	@vprusso	Claude Fable 5	2026-07-15
	[[390,82,27]]	generalized bicycle	390	82	d ≤ 27	153.277	·	16	@seunomonije	Claude Fable 5	2026-07-14
★	[[684,10,101]]	2BGA coset	684	10	d ≤ 101	149.137	·	12	@vprusso	Claude Opus 5	2026-08-09
★	[[574,252,18]]	lifted product	574	252	d ≤ 18	142.244	·	14	okada-kasai (reconstruction)		2026-08-05
★	[[492,170,20]]	lifted product	492	170	d ≤ 20	138.211	·	12	Okada et al.		2026
★	[[516,178,20]]	lifted product	516	178	d ≤ 20	137.984	·	12	Okada et al.		2026
★	[[390,68,28]]	generalized bicycle	390	68	d ≤ 28	136.697	·	13	@seunomonije	Claude Fable 5	2026-07-15
★	[[254,58,21]]	generalized bicycle	254	58	d ≤ 21	100.701	·	16	@seunomonije	Claude Fable 5	2026-07-17
★	[[254,44,24]]	generalized bicycle	254	44	d ≤ 24	99.78	·	16	@vprusso	Claude Fable 5	2026-07-14
★	[[700,140,22]]known params	balanced product	700	140	d ≤ 22	96.8	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[372,130,16]]known params	lifted product	372	130	d ≤ 16	89.462	·	12	Okada et al.		2026
★	[[684,8,85]]	other	684	8	d ≤ 85	84.503	·	8	@MathysRennela	Tencent Hy3	2026-07-18
★	[[584,150,18]]	lifted product	584	150	d ≤ 18	83.219	·	8	Okada et al.		2026
★	[[630,126,20]]	lifted product	630	126	d ≤ 20	80.0	·	9	Bhardwaj et al.		2026
★	[[625,125,20]]known params	balanced product	625	125	d ≤ 20	80.0	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[254,44,21]]	generalized bicycle	254	44	d ≤ 21	76.394	·	12	@vprusso	Claude Fable 5	2026-07-14
★	[[276,98,14]]known params	lifted product	276	98	d ≤ 14	69.594	·	12	Okada et al.		2026
★	[[550,110,18]]known params	balanced product	550	110	d ≤ 18	64.8	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[540,108,18]]	lifted product	540	108	d ≤ 18	64.8	·	9	Bhardwaj et al.		2026
★	[[525,105,18]]known params	balanced product	525	105	d ≤ 18	64.8	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[258,32,22]]	generalized bicycle	258	32	d ≤ 22	60.031	·	10	@willzeng	Claude Fable 5	2026-07-14
★	[[530,216,12]]known params	lifted product	530	216	d ≤ 12	58.687	·	10	Okada et al.		2026
★	[[590,240,12]]known params	lifted product	590	240	d ≤ 12	58.576	·	10	Okada et al.		2026
★	[[500,100,16]]	lifted product	500	100	d ≤ 16	51.2	·	9	Bhardwaj et al.		2026
★	[[390,78,16]]known params	balanced product	390	78	d ≤ 16	51.2	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[472,122,14]]known params	lifted product	472	122	d ≤ 14	50.661	·	8	Okada et al.		2026
★	[[488,126,14]]known params	lifted product	488	126	d ≤ 14	50.607	·	8	Okada et al.		2026
★	[[568,146,14]]	lifted product	568	146	d ≤ 14	50.38	·	8	@MathysRennela	Tencent Hy3	2026-07-16
★	[[210,24,20]]	generalized bicycle	210	24	d ≤ 20	45.714	·	10	@willzeng	Claude Fable 5	2026-07-14
★	[[320,64,14]]known params	balanced product	320	64	d ≤ 14	39.2	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[300,60,14]]	lifted product	300	60	d ≤ 14	39.2	·	9	Bhardwaj et al.		2026
★	[[576,292,8]]	other	576	292	d ≤ 8	32.444	·	12	@mathysrennela	Deepseek V4 Flash 0731	2026-08-05
★	[[310,14,26]]	generalized bicycle	310	14	d ≤ 26	30.529	·	10	@vprusso	Claude Opus 4.8	2026-07-24
★	[[240,48,12]]known params	balanced product	240	48	d ≤ 12	28.8	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[210,42,12]]known params	balanced product	210	42	d ≤ 12	28.8	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[200,40,12]]	lifted product	200	40	d ≤ 12	28.8	·	9	Bhardwaj et al.		2026
★	[[126,18,14]]	generalized bicycle	126	18	d ≤ 14	28.0	·	10	@willzeng	Claude Fable 5	2026-07-14
★	[[310,16,23]]	2BGA coset	310	16	d ≤ 23	27.303	·	9	@vprusso	Claude Opus 4.8	2026-08-02
★	[[240,16,20]]	2BGA coset	240	16	d ≤ 20	26.667	·	8	Aydin et al.		2026-07-14
★	[[336,20,21]]	2BGA coset	336	20	d ≤ 21	26.25	·	8	@willzeng	Claude Fable 5	2026-07-14
★	[[336,26,18]]	generalized bicycle	336	26	d ≤ 18	25.071	·	8	@seunomonije	Claude Fable 5	2026-07-14
★	[[210,26,14]]	generalized bicycle	210	26	d ≤ 14	24.267	·	8	@seunomonije	Claude Fable 5	2026-07-17
★	[[672,18,30]]	generalized bicycle	672	18	d ≤ 30	24.107	·	8	@vprusso	Claude Opus 4.8	2026-07-24
★	[[128,12,16]]	generalized bicycle	128	12	d ≤ 16	24.0	·	16	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-29
	[[336,20,20]]	generalized bicycle	336	20	d ≤ 20	23.81	·	8	@FarLab	Claude Fable 5	2026-07-08
★	[[168,20,14]]	2BGA coset	168	20	d ≤ 14	23.333	·	8	Aydin et al.		2026-06-15
	[[336,24,18]]	generalized bicycle	336	24	d ≤ 18	23.143	·	8	@seunomonije	Claude Fable 5	2026-07-14
	[[180,20,14]]	2BGA coset	180	20	d ≤ 14	21.778	·	8	@FarLab	Claude Opus 4.8	2026-06-22
★	[[168,16,15]]	2BGA coset	168	16	d ≤ 15	21.429	·	8	Aydin et al.		2026-06-15
★	[[420,10,30]]	2BGA coset	420	10	d ≤ 30	21.429	·	8	@vprusso	Claude Opus 4.8	2026-08-02
★	[[336,28,16]]	generalized bicycle	336	28	d ≤ 16	21.333	·	8	@seunomonije	Claude Fable 5	2026-07-20
★	[[330,34,14]]	generalized bicycle	330	34	d ≤ 14	20.194	·	8	@seunomonije	Claude Fable 5	2026-07-17
★	[[270,54,10]]	balanced product	270	54	d ≤ 10	20.0	·	9	@mathysrennela	Xiaomi Mimo-V2.5	2026-07-31
★	[[220,44,10]]	lifted product	220	44	d ≤ 10	20.0	·	9	@yhu1996	Claude Opus 4.8	2026-08-05
★	[[160,32,10]]known params	balanced product	160	32	d ≤ 10	20.0	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[150,30,10]]known params	balanced product	150	30	d ≤ 10	20.0	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[310,14,21]]	generalized bicycle	310	14	d ≤ 21	19.916	·	8	@shassinger	OpenAI 5.6 Sol	2026-07-14
	[[180,18,14]]	2BGA coset	180	18	d ≤ 14	19.6	·	8	@FarLab	Claude Opus 4.8	2026-06-22
★	[[360,12,24]]known params	bivariate bicycle	360	12	d ≤ 24	19.2	·	6	Zijian Liang et al.		2025
	[[240,14,18]]	2BGA coset	240	14	d ≤ 18	18.9	·	8	@vprusso	Claude Opus 4.8	2026-08-04
★	[[252,130,6]]	other	252	130	d ≤ 6	18.571	·	12	@mathysrennela	Deepseek V4 Flash 0731	2026-08-05
★	[[376,6,32]]	lifted product	376	6	d ≤ 32	16.34	·	10	@vprusso	Claude Opus 5	2026-08-07
	[[248,10,20]]	2BGA coset	248	10	d ≤ 20	16.129	·	8	@vprusso	Claude Opus 4.8	2026-08-02
★	[[192,12,16]]	2BGA coset	192	12	d ≤ 16	16.0	·	8	@vprusso	Claude Opus 4.8	2026-08-03
★	[[288,8,24]]	2BGA coset	288	8	d ≤ 24	16.0	·	8	@vprusso	Claude Opus 4.8	2026-08-02
★	[[340,16,18]]known params	bivariate bicycle	340	16	d ≤ 18	15.247	·	6	Zijian Liang et al.		2025
★	[[320,6,28]]	generalized bicycle	320	6	d ≤ 28	14.7	·	8	@FarLab	Claude Opus 4.8	2026-07-06
★	[[264,8,22]]	2BGA coset	264	8	d ≤ 22	14.667	·	7	@vprusso	Claude Opus 4.8	2026-08-04
★	[[140,8,16]]	generalized bicycle	140	8	d ≤ 16	14.629	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-29
	[[280,10,20]]	2BGA coset	280	10	d ≤ 20	14.286	·	8	@vprusso	Claude Opus 4.8	2026-08-03
★	[[126,28,8]]	generalized bicycle	126	28	d = 8	14.222	·	10	Panteleev et al.		2019-04-04
★	[[288,16,16]]	generalized bicycle	288	16	d ≤ 16	14.222	·	6	@willzeng	Claude Fable 5	2026-07-14
★	[[576,8,32]]	lifted product	576	8	d ≤ 32	14.222	·	10	@vprusso	Claude Opus 5	2026-08-07
★	[[144,8,16]]	generalized bicycle	144	8	d ≤ 16	14.222	·	10	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-29
★	[[128,8,15]]	generalized bicycle	128	8	d ≤ 15	14.062	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-28
★	[[330,8,24]]known params	bivariate bicycle	330	8	d ≤ 24	13.964	·	6	Zijian Liang et al.		2025
★	[[592,8,32]]	lifted product	592	8	d ≤ 32	13.838	·	8	@vprusso	Claude Opus 5	2026-08-07
★	[[288,12,18]]	bivariate bicycle	288	12	d ≤ 18	13.5	·	6	Bravyi et al.		2023-08-15
★	[[144,6,18]]	generalized bicycle	144	6	d ≤ 18	13.5	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-29
	[[240,8,20]]	2BGA coset	240	8	d ≤ 20	13.333	·	8	@vprusso	Claude Opus 4.8	2026-07-31
★	[[348,4,34]]	lifted product	348	4	d ≤ 34	13.287	·	10	@vprusso	Claude Opus 5	2026-08-07
★	[[132,6,17]]	generalized bicycle	132	6	d ≤ 17	13.136	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-29
★	[[310,6,26]]	lifted product	310	6	d ≤ 26	13.084	·	9	@vprusso	Claude Opus 5	2026-08-06
★	[[248,10,18]]known params	bivariate bicycle	248	10	d ≤ 18	13.065	·	6	Zijian Liang et al.		2025
★	[[230,46,8]]	lifted product	230	46	d ≤ 8	12.8	·	9	@yhu1996	Claude Opus 4.8	2026-08-05
★	[[195,39,8]]	lifted product	195	39	d ≤ 8	12.8	·	9	@yhu1996	Claude Opus 4.8	2026-08-04
★	[[190,38,8]]	lifted product	190	38	d ≤ 8	12.8	·	9	@yhu1996	Claude Opus 4.8	2026-08-04
★	[[180,36,8]]	lifted product	180	36	d ≤ 8	12.8	·	9	@yhu1996	Claude Opus 4.8	2026-08-04
★	[[170,34,8]]	lifted product	170	34	d ≤ 8	12.8	·	9	@yhu1996	Claude Opus 4.8	2026-08-04
★	[[120,24,8]]	lifted product	120	24	d ≤ 8	12.8	·	9	@yhu1996	Claude Opus 4.8	2026-08-04
★	[[100,20,8]]known params	balanced product	100	20	d = 8	12.8	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[120,6,16]]	generalized bicycle	120	6	d ≤ 16	12.8	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-28
	[[136,6,17]]	generalized bicycle	136	6	d ≤ 17	12.75	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-29
★	[[312,8,22]]known params	bivariate bicycle	312	8	d ≤ 22	12.41	·	6	Zijian Liang et al.		2025
★	[[252,12,16]]known params	bivariate bicycle	252	12	d ≤ 16	12.19	·	6	Zijian Liang et al.		2025
	[[126,6,16]]	generalized bicycle	126	6	d ≤ 16	12.19	·	12	@mathysrennela	Xiaomi MiMo-V2.5	2026-07-28
	[[240,13,15]]	generalized bicycle	240	13	d ≤ 15	12.188	·	8	@FarLab	Claude Fable 5	2026-07-08
★	[[144,12,12]]	bivariate bicycle	144	12	d = 12	12.0	·	6	Bravyi et al.		2023-08-15
★	[[270,8,20]]known params	bivariate bicycle	270	8	d ≤ 20	11.852	·	6	Zijian Liang et al.		2025
★	[[350,6,26]]known params	bivariate bicycle	350	6	d ≤ 26	11.589	·	6	Zijian Liang et al.		2025
★	[[308,6,24]]known params	bivariate bicycle	308	6	d ≤ 24	11.221	·	6	Zijian Liang et al.		2025
★	[[288,50,8]]	bivariate bicycle	288	50	d ≤ 8	11.111	·	8	Cruz-Benito et al.		2026-06-01
★	[[324,4,30]]	lifted product	324	4	d ≤ 30	11.111	·	10	@vprusso	Claude Opus 5	2026-08-06
★	[[234,8,18]]known params	bivariate bicycle	234	8	d ≤ 18	11.077	·	6	Zijian Liang et al.		2025
★	[[266,6,22]]known params	bivariate bicycle	266	6	d ≤ 22	10.917	·	6	Zijian Liang et al.		2025
★	[[660,8,30]]	lifted product	660	8	d ≤ 30	10.909	·	7	@vprusso	Claude Opus 5	2026-08-06
★	[[224,6,20]]known params	bivariate bicycle	224	6	d ≤ 20	10.714	·	6	Zijian Liang et al.		2025
★	[[182,6,18]]known params	bivariate bicycle	182	6	d ≤ 18	10.681	·	6	Zijian Liang et al.		2025
	[[288,48,8]]	bivariate bicycle	288	48	d ≤ 8	10.667	·	10	Cruz-Benito et al.		2026-06-01
★	[[192,8,16]]known params	bivariate bicycle	192	8	d ≤ 16	10.667	·	6	Zijian Liang et al.		2025
★	[[186,10,14]]known params	bivariate bicycle	186	10	d ≤ 14	10.538	·	6	Zijian Liang et al.		2025
★	[[128,21,8]]	generalized bicycle	128	21	d ≤ 8	10.5	·	8	@mathysrennela	Xiaomi Mimo-V2.5	2026-07-30
	[[288,46,8]]	bivariate bicycle	288	46	d ≤ 8	10.222	·	8	Cruz-Benito et al.		2026-06-01
★	[[128,13,10]]	generalized bicycle	128	13	d ≤ 10	10.156	·	8	@mathysrennela	Xiaomi Mimo-V2.5	2026-07-30
★	[[154,6,16]]known params	bivariate bicycle	154	6	d ≤ 16	9.974	·	6	Zijian Liang et al.		2025
	[[294,8,19]]	generalized bicycle	294	8	d ≤ 19	9.823	·	8	@FarLab	Gemini 3.1 Pro	2026-07-01
★	[[300,4,27]]	lifted product	300	4	d ≤ 27	9.72	·	9	@vprusso	Claude Opus 5	2026-08-06
★	[[162,8,14]]known params	bivariate bicycle	162	8	d ≤ 14	9.679	·	6	Zijian Liang et al.		2025
★	[[120,8,12]]known params	bivariate bicycle	120	8	d = 12	9.6	·	6	@FarLab	Claude Opus 4.8	2026-06-26
★	[[384,12,17]]	bivariate bicycle2D-local bilayer	384	12	d ≤ 17	9.031	0.0045	8	@mathysrennela	DeepSeek V4 Flash 0731	2026-08-09
★	[[64,16,6]]	2BGA coset	64	16	d = 6	9.0	·	10	@vprusso	Claude Opus 4.8	2026-08-04
★	[[54,6,9]]known params	2BGA coset	54	6	d = 9	9.0	·	8	Lin et al.		2023
★	[[90,8,10]]	bivariate bicycle	90	8	d = 10	8.889	·	6	Bravyi et al.		2023-08-15
★	[[354,4,28]]known params	bivariate bicycle	354	4	d ≤ 28	8.859	·	6	Zijian Liang et al.		2025
★	[[98,6,12]]known params	bivariate bicycle	98	6	d = 12	8.816	·	6	Zijian Liang et al.		2025
★	[[263,16,12]]	bivariate bicycle2D-local bilayer	263	16	d ≤ 12	8.76	0.014	8	@FarLab	Claude Fable 5	2026-07-09
	[[360,16,14]]	bivariate bicycle	360	16	d ≤ 14	8.711	·	6	@cbjuan	Claude Opus 4.6 +2	2026-08-05
★	[[318,4,26]]known params	bivariate bicycle	318	4	d ≤ 26	8.503	·	6	Zijian Liang et al.		2025
★	[[216,15,11]]	bivariate bicycle2D-local bilayer	216	15	d = 11	8.403	0.01	8	@FarLab	Claude Fable 5	2026-07-08
★	[[140,6,14]]known params	bivariate bicycle	140	6	d ≤ 14	8.4	·	6	Zijian Liang et al.		2025
★	[[276,4,24]]known params	bivariate bicycle	276	4	d ≤ 24	8.348	·	6	Zijian Liang et al.		2025
★	[[294,12,14]]	tile2D-local bilayer	294	12	d ≤ 14	8.0	0.004	8	@vprusso	Claude Opus 4.8	2026-06-25
★	[[246,4,22]]known params	bivariate bicycle	246	4	d ≤ 22	7.87	·	6	Zijian Liang et al.		2025
★	[[204,4,20]]known params	bivariate bicycle	204	4	d ≤ 20	7.843	·	6	Zijian Liang et al.		2025
★	[[174,4,18]]known params	bivariate bicycle	174	4	d ≤ 18	7.448	·	6	Zijian Liang et al.		2025
	[[108,8,10]]	bivariate bicycle	108	8	d = 10	7.407	·	6	Bravyi et al.		2023-08-15
	[[240,12,12]]	2BGA coset	240	12	d = 12	7.2	·	6	@vprusso	Claude Opus 4.8	2026-07-31
★	[[60,12,6]]known params	balanced product	60	12	d = 6	7.2	·	9	@yifanhong	GPT 5.6 Sol	2026-08-02
★	[[80,9,8]]known params	2BGA coset2D-local bilayer	80	9	d = 8	7.2	0.0092	8	Lin et al.		2023
	[[140,10,10]]	generalized bicycle	140	10	d = 10	7.143	·	8	@mathysrennela	Tencent Hy3	2026-07-18
★	[[84,6,10]]known params	bivariate bicycle	84	6	d = 10	7.143	·	6	Zijian Liang et al.		2025
★	[[242,12,12]]	bivariate bicycle2D-local bilayer	242	12	d ≤ 12	7.14	0.0035	8	@MathysRennela	DeepSeek V4 Flash 0731	2026-08-07
★	[[288,32,8]]	bivariate bicycle	288	32	d ≤ 8	7.111	·	6	@cbjuan	Claude Opus 4.6 +2	2026-08-05
★	[[144,16,8]]	bivariate bicycle	144	16	d = 8	7.111	·	6	@cbjuan	Claude Opus 4.6 +2	2026-08-05
	[[281,121,4]]	hypergraph product	281	121	d ≤ 4	6.89	·	21	@mathysrennela	Tencent Hy3	2026-07-17
★	[[114,4,14]]known params	bivariate bicycle	114	4	d ≤ 14	6.877	·	6	Zijian Liang et al.		2025
★	[[360,24,10]]	bivariate bicycle	360	24	d ≤ 10	6.667	·	6	@cbjuan	Claude Opus 4.6 +2	2026-08-05
★	[[183,12,10]]	bivariate bicycle2D-local bilayer	183	12	d ≤ 10	6.557	0.0032	8	@MathysRennela	DeepSeek V4 Flash 0731	2026-08-07
	[[240,8,14]]	2BGA coset	240	8	d ≤ 14	6.533	·	6	@vprusso	Claude Opus 4.8	2026-07-31
	[[80,8,8]]known params	2BGA coset	80	8	d = 8	6.4	·	8	Lin et al.		2023
★	[[288,48,6]]	bivariate bicycle	288	48	d ≤ 6	6.0	·	6	@cbjuan	Claude Opus 4.6 +2	2026-08-05
★	[[144,24,6]]	bivariate bicycle	144	24	d ≤ 6	6.0	·	6	@cbjuan	Claude Opus 4.6 +2	2026-08-05
★	[[128,12,8]]	2BGA coset	128	12	d = 8	6.0	·	6	@vprusso	Claude Opus 4.8	2026-08-04
★	[[72,12,6]]	bivariate bicycle2D-local bilayer	72	12	d = 6	6.0	0.0136	6	Bravyi et al.		2023-08-15
★	[[16,6,4]]known params	other2D-local single	16	6	d = 4	6.0	0.359	8	@FarLab	Claude Opus 5	2026-07-25
★	[[96,4,12]]known params	bivariate bicycle	96	4	d = 12	6.0	·	6	Zijian Liang et al.		2025
★	[[62,10,6]]known params	bivariate bicycle2D-local bilayer	62	10	d = 6	5.806	0.0344	6	Zijian Liang et al.		2025
★	[[70,6,8]]known params	bivariate bicycle	70	6	d = 8	5.486	·	6	Zijian Liang et al.		2025
★	[[72,8,7]]	2BGA coset	72	8	d = 7	5.444	·	6	@vprusso	Claude Opus 4.8	2026-08-04
★	[[48,4,8]]known params	bivariate bicycle2D-local bilayer	48	4	d = 8	5.333	0.0046	6	Zijian Liang et al.		2025
★	[[56,6,7]]	2BGA coset	56	6	d = 7	5.25	·	6	@vprusso	Claude Opus 4.8	2026-08-04
★	[[78,4,10]]known params	bivariate bicycle	78	4	d = 10	5.128	·	6	Zijian Liang et al.		2025
★	[[60,8,6]]known params	bivariate bicycle	60	8	d = 6	4.8	·	6	Zijian Liang et al.		2025
★	[[30,4,6]]known params	bivariate bicycle	30	4	d = 6	4.8	·	6	Zijian Liang et al.		2025
★	[[148,44,4]]	hypergraph product	148	44	d ≤ 4	4.757	·	20	@mathysrennela	Tencent Hy3	2026-07-17
★	[[392,8,15]]known params	bivariate bicycle2D-local bilayer	392	8	d ≤ 15	4.592	0.0717	6	@mathysrennela	Tencent Hy3	2026-07-15
★	[[241,121,3]]	hypergraph product	241	121	d ≤ 3	4.519	·	12	@mathysrennela	Tencent Hy3	2026-07-17
	[[88,8,7]]	2BGA coset	88	8	d = 7	4.455	·	6	@vprusso	Claude Opus 4.8	2026-07-31
★	[[15,7,3]]known params	other2D-local single	15	7	d = 3	4.2	0.343	8	@FarLab	Claude Opus 5	2026-07-25
★	[[232,104,3]]	hypergraph product	232	104	d ≤ 3	4.034	·	19	@mathysrennela	Tencent Hy3	2026-07-17
★	[[192,12,8]]	bivariate bicycle2D-local bilayer	192	12	d = 8	4.0	0.0237	6	@FarLab	Claude Opus 5	2026-07-25
★	[[288,8,12]]	bivariate bicycle2D-local bilayer	288	8	d = 12	4.0	0.0625	6	Liang et al.		2025-04-11
★	[[32,8,4]]known params	2BGA coset	32	8	d = 4	4.0	·	8	Lin et al.		2023
★	[[24,6,4]]	generalized bicycle2D-local bilayer	24	6	d = 4	4.0	0.0816	6	Lin et al.		2023-06-28
	[[292,18,8]]known params	bivariate bicycle	292	18	d = 8	3.945	·	6	Zijian Liang et al.		2025
★	[[40,6,5]]	generalized bicycle	40	6	d = 5	3.75	·	6	Lin et al.		2023-06-28
★	[[18,4,4]]known params	bivariate bicycle2D-local single	18	4	d = 4	3.556	0.0988	6	Zijian Liang et al.		2025
★	[[336,6,14]]	bivariate bicycle2D-local bilayer	336	6	d ≤ 14	3.5	0.0121	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[201,78,3]]	hypergraph product	201	78	d ≤ 3	3.493	·	19	@mathysrennela	Tencent Hy3	2026-07-17
★	[[117,44,3]]	hypergraph product	117	44	d ≤ 3	3.385	·	11	@mathysrennela	Tencent Hy3	2026-07-17
★	[[180,6,10]]	bivariate bicycle2D-local bilayer	180	6	d = 10	3.333	0.0115	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[264,6,12]]	bivariate bicycle2D-local bilayer	264	6	d = 12	3.273	0.0113	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[200,8,9]]	bivariate bicycle2D-local bilayer	200	8	d = 9	3.24	0.0506	6	Liang et al.		2025-04-11
	[[360,32,6]]	bivariate bicycle	360	32	d ≤ 6	3.2	·	8	@cbjuan	Claude Opus 4.6 +2	2026-08-05
★	[[125,25,4]]	balanced product	125	25	d ≤ 4	3.2	·	9	@MathysRennela	OpenAI GPT-5.6 Luna	2026-08-07
	[[80,16,4]]	hypergraph product	80	16	d = 4	3.2	·	12	@mathysrennela	Tencent Hy3	2026-07-17
★	[[160,6,9]]	bivariate bicycle2D-local bilayer	160	6	d = 9	3.038	0.0105	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[240,6,11]]	bivariate bicycle2D-local bilayer	240	6	d = 11	3.025	0.0105	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[128,6,8]]	bivariate bicycle2D-local bilayer	128	6	d = 8	3.0	0.0104	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
	[[72,6,6]]	bivariate bicycle2D-local bilayer	72	6	d = 6	3.0	0.0104	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
	[[198,12,7]]	bivariate bicycle2D-local bilayer	198	12	d = 7	2.97	0.0074	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[102,33,3]]	hypergraph product	102	33	d = 3	2.912	·	11	@mathysrennela	Tencent Hy3	2026-07-17
★	[[299,5,13]]	bivariate bicycle2D-local bilayer	299	5	d = 13	2.826	0.0283	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[170,52,3]]	hypergraph product	170	52	d ≤ 3	2.753	·	19	@mathysrennela	Tencent Hy3	2026-07-17
★	[[91,5,7]]	bivariate bicycle2D-local bilayer	91	5	d = 7	2.692	0.0269	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[120,5,8]]	bivariate bicycle2D-local bilayer	120	5	d = 8	2.667	0.0267	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[153,5,9]]	bivariate bicycle2D-local bilayer	153	5	d = 9	2.647	0.0265	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[112,6,7]]	bivariate bicycle2D-local bilayer	112	6	d = 7	2.625	0.0091	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
★	[[231,5,11]]	bivariate bicycle2D-local bilayer	231	5	d = 11	2.619	0.0262	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[58,16,3]]	hypergraph product	58	16	d = 3	2.483	·	7	@mathysrennela		2026-07-17
	[[88,6,6]]	bivariate bicycle2D-local bilayer	88	6	d = 6	2.455	0.0303	6	Liang et al.		2025-04-11
★	[[65,17,3]]	hypergraph product	65	17	d = 3	2.354	·	8	@mathysrennela	Tencent Hy3	2026-07-18
	[[56,2,8]]	generalized bicycle	56	2	d = 8	2.286	·	6	Wang et al.		2022-03-31
★	[[87,22,3]]	hypergraph product	87	22	d = 3	2.276	·	11	@mathysrennela	Tencent Hy3	2026-07-17
	[[128,8,6]]	bivariate bicycle2D-local bilayer	128	8	d = 6	2.25	0.0352	6	Liang et al.		2025-04-11
★	[[51,12,3]]	hypergraph product	51	12	d = 3	2.118	·	7	@mathysrennela	Tencent Hy3	2026-07-17
★	[[64,2,8]]	topological2D-local single	64	2	d = 8	2.0	0.125	4	Kitaev, A. Yu.		1997-07-09
★	[[36,2,6]]	topological2D-local single	36	2	d = 6	2.0	0.125	4	Kitaev, A. Yu.		1997-07-09
★	[[16,2,4]]	topological2D-local single	16	2	d = 4	2.0	0.125	4	Kitaev, A. Yu.		1997-07-09
	[[146,18,4]]known params	bivariate bicycle	146	18	d = 4	1.973	·	6	Zijian Liang et al.		2025
	[[50,6,4]]	bivariate bicycle2D-local bilayer	50	6	d = 4	1.92	0.0768	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-16
	[[66,5,5]]	bivariate bicycle2D-local bilayer	66	5	d = 5	1.894	0.0189	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[45,9,3]]	hypergraph product	45	9	d = 3	1.8	·	5	@mathysrennela		2026-07-17
	[[45,5,4]]	bivariate bicycle2D-local bilayer	45	5	d = 4	1.778	0.0219	6	@FarLab and @vprusso	Claude Opus 4.8	2026-06-19
★	[[42,8,3]]	generalized bicycle	42	8	d = 3	1.714	·	6	Wang et al.		2022-03-31
★	[[14,6,2]]known params	bivariate bicycle2D-local single	14	6	d = 2	1.714	0.0406	6	Zijian Liang et al.		2025
★	[[37,7,3]]	topological2D-local single	37	7	d = 3	1.703	0.489	6	@mathysrennela	OpenAI GPT-5.6 Luna	2026-08-02
★	[[12,4,2]]known params	bivariate bicycle2D-local single	12	4	d = 2	1.333	0.109	6	Zijian Liang et al.		2025
★	[[37,1,7]]known params	topological2D-local single	37	1	d = 7	1.324	0.38	6	@FarLab	Claude Opus 5	2026-07-26
★	[[19,1,5]]known params	topological2D-local single	19	1	d = 5	1.316	0.378	6	@FarLab	Claude Opus 5	2026-07-26
★	[[7,1,3]]	topological2D-local single	7	1	d = 3	1.286	0.321	4	Steane, Andrew M.		1996-01-29
★	[[81,1,9]]	topological2D-local single	81	1	d = 9	1.0	1	4	Kitaev, A. Yu.		1997-07-09
★	[[49,1,7]]	topological2D-local single	49	1	d = 7	1.0	1	4	Kitaev, A. Yu.		1997-07-09
★	[[25,1,5]]	topological2D-local single	25	1	d = 5	1.0	1	4	Kitaev, A. Yu.		1997-07-09
★	[[625,50,3]]	topological2D-local single	625	50	d = 3	0.72	0.72	4	@aarontrowbridge	Kimi K3 (Amicode)	2026-08-07
★	[[361,26,3]]	topological2D-local single	361	26	d ≤ 3	0.648	0.648	4	@mathysrennela	DeepSeek V4 Flash 0731	2026-08-09
★	[[169,10,3]]	topological2D-local single	169	10	d ≤ 3	0.533	0.532	4	@mathysrennela	DeepSeek V4 Flash 0731	2026-08-09

Leaderboard

10 contributors · 147 codes submitted through the challenge4 of 10 contributors have a code with a verified layout and d ≥ 3

best kd²/n

534.324

[[482,146,42]] · d≤42 · w=28 · @yhu1996

best g

0.72

[[625,50,3]] · d=3 · r=1.4142 · ρ=1 · @aarontrowbridge

Participate

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

git clone https://github.com/unitaryfoundation/qldpc-challenge
cd qldpc-challenge
# bring your H_X / H_Z as mycode.npz (keys hx, hz)
./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