crystal-thresholds

Code and data for calculating the thresholds of the fault-tolerant cluster states used in the research paper https://arxiv.org/abs/1909.11817

The C++ code needs to be compiled with g++ before use. It depends on external packages that cannot be reditributed in this repository, and have to be manually installed.

A random number generator and a minimum weight perfect matching package are necessary to run these simulations.

For random number generation, we recommend the Marsenne twister RngStreams for C++. If you want to use it, create a directory contrib/RngStream and place the files RngStream.h and RngStream.cpp there:

cd contrib
mkdir RngStream
cd RngStream
curl http://www.iro.umontreal.ca/~lecuyer/myftp/streams00/c++/RngStream.h -o RngStream.h
curl http://www.iro.umontreal.ca/~lecuyer/myftp/streams00/c++/RngStream.cpp -o RngStream.cpp

For perfect matching, we recommend Blossom V, which is available for non-commercial research purposes. If you want to use it, unpack it into the contrib/ directory to create a folder blossom5-v2.05.src with the required contents.

cd contrib
curl https://pub.ista.ac.at/~vnk/software/blossom5-v2.05.src.tar.gz -o blossom5-v2.05.src.tar.gz
tar xf blossom5-v2.05.src.tar.gz

Note: If you need to calculate this kind of threshold for commercial purposes, you will need to acquire your own replacements for these external packages, and change the code accordingly. Moreover, I will not be able to assist you if you intend to use this software for commercial purposes.

The script src/MWPM/make.sh compiles the binaries and populates the bin/ folder:

cd src/MWPM
sh make.sh

It creates one binary per lattice in bin/. The threshold for each lattice requires many runs of the simulations, and so these binaries are best executed in a cluster.

The data at lib/lattices and lib/tilings was extracted from sytre and Gavrog.

It is converted into C++ files with the Python script at lib/src/make.py.

Call the binary that is appropriate for the lattice that you want to simulate with:

./bin/mwpm-[lattice] [L] [p_x] [p_z] [p_spam] [trials] [red_edge] > [output_file]

The parameters are:

• L : Side size of the cluster.
• p_x : X error probability.
• p_z : Z error probability.
• p_spam : SPAM error probability.
• trials : Number of trials to run.
• red_edge : One of the following: none, fixed, sequential, or random.

The output is sent to stdout, so > [output_file] writes it to your desired location.