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quantumlib / OpenFermion

The electronic structure package for quantum computers.
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Inconsistent bits for rotations in DF and THC resource estimates #766

Closed wpol-psiq closed 1 year ago

wpol-psiq commented 2 years ago

In both the double-factorization and tensor hypercontraction versions of qubitization detailed in the THC paper, we often need to load angles or coefficients into our computation. These angles need to be represented by some number of bits; in this paper in particular, we have aleph and beth.

In the DF and THC cost estimate scripts in OpenFermion, the cost functions take these values as arguments rather than compute them using equations found in the paper (like aleph = ceil(2.5 + log(10*lambda/eps)) on pg. 16 just under Eq. 33). I have noticed that the values one gets for these bits when using the equations in the paper and the chosen values for these bits in some FeMoco test estimates differ from each other somewhat. It does not seem like such a big difference, but leads (in some cases) to a 5x-10x difference in Toffoli cost for these algorithms.

Is there a reason for the particular choices of these values in these test scripts for FeMoco, and if so, why does it differ from the expressions in the paper?

ncrubin commented 1 year ago

just as the cutoffs for these factorizations can be numerically determined so can the bits of precision. For the THC paper I believe this is what they did...but I'm not sure.