ZKSF

Zero Kelvin Simulation Foundry

ZCC-Estimate-v0.2

2026-09-12T19:37:09+00:00

Certificate of Simulation Accuracy

Certificate ID

66e9fabc9e784425

Result recorded

Engine

neural.tpu

Method

nnqs.vmc

Shots

1024

How this certificate was produced

This result comes from a neural network quantum state: a wavefunction represented by a neural network and optimised by variational Monte Carlo, rather than by contracting a circuit. It is the class of simulator used to reach states whose entanglement does not follow an area law, where tensor networks fail, and it is normally published with no accuracy statement at all.
The accuracy statement here is not added afterwards. Variational Monte Carlo already measures the energy variance of the state it is training, and that variance is what bounds the answer, so the bound costs nothing beyond the run itself and cannot be omitted from it.
The ceiling is unconditional. The variational principle gives >= E_ground for every set of parameters, so the true ground-state energy is at most -10.2499758. That holds whatever the optimiser did, whether or not it converged, and needs no assumption about the spectrum. It is widened by five standard errors of the sampled mean so ordinary Monte Carlo fluctuation cannot breach it.
The lower figure is not a bound of the same kind and is reported as a diagnostic rather than a guarantee. -10.28194421 follows from Weinstein's inequality applied to the measured energy variance, and holds only while the trial state lies nearer the ground state than the first excited state. A run cannot verify that about itself. Independent restarts converging to the same energy is evidence, and is recorded on this certificate; it is not proof.
The measured energy variance is 0.000553322. A variance at or near zero identifies an eigenstate, not necessarily the ground state: a run that has settled onto an excited level reports near-zero variance and a confident interval around the wrong energy. That failure was reproduced from three independent causes during development, and it is why the two figures above are stated separately rather than as one symmetric interval.
A run whose Markov chains had not mixed is refused rather than certified. When the sampling is invalid the reported energy is not an expectation value under the state's own distribution, so neither figure above applies to it, and a number carrying a bound that does not hold is worse than no number at all. This certificate exists because that check passed.

Hamiltonian SHA-256: 3122be90f9ccce5b6aa7cda69f40899cf941975bd1f7af87af65bf431316806e