Instance: 8 sites, frustrated Gaussian couplings, seed 229, 2,000,000 source decays simulated.
| decays consumed | KL(empirical, exact) | total variation |
|---|---|---|
| 1,000 | 2.93e-01 | 0.164 |
| 2,000 | 1.37e-01 | 0.093 |
| 4,000 | 7.17e-02 | 0.078 |
| 8,000 | 4.61e-02 | 0.071 |
| 16,000 | 2.35e-02 | 0.032 |
| 32,000 | 1.47e-02 | 0.028 |
| 64,000 | 7.09e-03 | 0.017 |
| 128,000 | 3.47e-03 | 0.016 |
| 256,000 | 1.94e-03 | 0.011 |
| 512,000 | 8.54e-04 | 0.006 |
| 1,024,000 | 5.15e-04 | 0.005 |
Final KL divergence after 2,000,000 decays: 5.15e-04 over all 256 states. The machine samples the exact distribution its couplings define.
- integrated autocorrelation time: 25.9 decays
- effective independent samples drawn: 76,707
- decays per independent sample: 26
- optimization mode (annealed): median 173 decays to first reach the true ground state (25/25 runs reached it)
| carrier | J per quantum | J per sample | vs MTJ p bit (33 fJ/sample) |
|---|---|---|---|
| 229mTh quantum (8.4 eV) | 1.34e-18 | 3.49e-17 | 945x cheaper |
| 57Fe quantum (14.4 keV) | 2.31e-15 | 6.02e-14 | 2x costlier |
| 60Co gamma (1.25 MeV) | 2.00e-13 | 5.22e-12 | 158x costlier |
The table is the energy honesty argument of the foundational document, now with measured constants: at MeV quanta the sampler cannot compete; at the 8.4 eV transition the same machine undercuts engineered probabilistic silicon, because the source energy is spent either way and each decay is a genuine random number no transistor had to synthesize.