Max-Cut at 16.5 Billion to 200 Billion Variables on One 8×H100 Node
To our knowledge the largest max-cut instance ever solved. Every reported cut is recomputed from the saved solution in exact integer arithmetic on the CPU, with no code shared with the solver, and the proof bundles carry hashes.
16.5 billionvariables (mean degree 3): 89.4392% of 2.475×10¹⁰ edges cut; recount difference 3.2×10⁻⁷
200 billionvariables, 6×10¹¹ edges: 77.42% cut in 11.4 h (quench solution at 73.39% recounted in 21.4 s)
0.0027 ppspread over 4 independent 10¹⁰-variable instances (79.5930–79.5957%)
0.0006 pp1 GPU vs 2-GPU sharded, same instance and schedule (N = 10⁸)
| Run (mean degree) | Solver (float32) | Recount (exact) | Relative difference |
|---|---|---|---|
| 1.65×10¹⁰ (3) | 2.21362×10¹⁰ | 22,136,207,143 | 3.2×10⁻⁷ |
| 1.03×10¹⁰ (6) | 2.45949×10¹⁰ | 24,594,910,829 | 4.4×10⁻⁷ |
| 10¹⁰ instance 1, seed 1 | 2.38787×10¹⁰ | 23,878,697,460 | 1.1×10⁻⁷ |
| 10¹⁰ instance 1, seed 2 | 2.38787×10¹⁰ | 23,878,706,730 | 2.8×10⁻⁷ |
| 10¹⁰ instance 3 | 2.38780×10¹⁰ | 23,877,997,940 | 8.6×10⁻⁸ |
| 10¹⁰ instance 4 | 2.38779×10¹⁰ | 23,877,908,021 | 3.4×10⁻⁷ |
| 10¹⁰ instance 5 | 2.38779×10¹⁰ | 23,877,943,348 | 1.8×10⁻⁶ |
| 2×10¹¹ quench bundle | 440,350,966,067 | 440,350,966,067 | 0 |
| 5×10¹⁰ quench bundle | 110,087,659,633 | 110,087,659,633 | 0 |
| Control: instance 3 spins on instance 1 | none | 49.9998% (random) | no match |
- Graph held in GPU memory: 1.03×10¹⁰ (degree 6) and 1.65×10¹⁰ (degree 3) variables; 2×10¹⁰ ran out of memory
- Regenerated edges reach 2×10¹¹ variables; the price is sweeps (77.42% vs 79.596%)
- Recounts agree with the solver within 1.8×10⁻⁶ (float32); proof bundles match exactly
- Sharding adds capacity at equal quality per sweep