Thanks to our volunteers we have more results to report. We have finished the computations for the 96-variable benchmark problems.

In the next figure the median minimum energy gap results for up to N=96 variable benchmark problems run on AQUA@home are shown.

For 8 and 16 variable cases, the results of both exact diagonalization and discrete imaginary time Quantum Monte Carlo (QMC) approaches are presented. In this cases the QMC approach is systematically over-predicting the minimum gaps by about 10%. This is because of a systematic error that arises from a discretization step which is understood and not expected to affect the scaling of either the gap or the runtime (although it will change the magnitude—here we see that an effect on the order of ~10% is reasonable).

It is not practical to calculate the minumum energy gap for N=32 and higher using diagonalization, so we are reporting the QMC results only.

If the data can be fit with a straight line on a log-log plot, it is consistent with a polynomial increase in runtime as the problems increase in size. The red line here is a straight line fit through the data, included to guide the eye. So far for this problem type the data from the computational experiment (at least up to N=96) is consistent with a polynomial increase in runtime (ie. the problems are predicted to take only a small amount longer for 96 variables than 8 variables). We are currently analyzing all of the data from the run and are close to having a draft scientific paper describing the experiment and the results you have helped generate.




Thanks again everybody for your support!

Geordie