runtime performance of Julia vs c++ DMRG

Question

Can you provide any preliminary data on Julia vs C++ runtime for iTensor’s DMRG? Is the algorithm implemented in Julia the same 2-site algorithm implemented in Julia?

Comments

Yes, it is the same algorithm between the two version. We hope to do some systematic benchmarking soon, but in general we have seen the Julia version is anywhere from 5% slower to 100% slower, depending on the problem and bond dimension.

Answer 1

Hi Matthew,
We now have publicly available benchmarks of both the C++ and Julia version of ITensor, including DMRG benchmarks but also algorithms like TRG (http://tensornetwork.org/trg/) and corner-transfer renormalization group (CTMRG). Here is the link:
https://github.com/ITensor/ITensorsBenchmarks.jl

If you specifically look at the plots subfolder you can see some comparison graphs:
https://github.com/ITensor/ITensorsBenchmarks.jl/tree/main/benchmarks/julia_vs_c%2B%2B/plots

The summary of what we've observed is that the Julia version is always very competitive with the C++ version, and typically even exceeds the C++ version's performance. We aren't totally sure why this is, but could include lots of effort by ITensor lead developer Matt Fishman to optimize the Julia version, and our use of high-quality Julia libraries for which we don't have an analogue in C++. Plus in some sense the Julia version got a head start by being based on years of effort designing and optimizing the C++ version.

We plan to put these benchmark results into the published version of the ITensor Paper (https://arxiv.org/abs/2007.14822) and give a more thorough discussion of them there.

Best regards,
Miles