An implementation of a large variety of Suzuki-Trotter decomposition schemes (or splitting methods).
This repository contains the scripts and data required to reproduce the results presented in "Optimised Trotter Decompositions for Classical and Quantum Computing", arXiv:2211.02691 [quant-ph], J. Phys. A: Math. Theor., DOI: 10.1088/1751-8121/acde7a as well as "Simple Ways to improve Discrete Time Evolution", arXiv:2309.03389 [quant-ph], LATTICE 2023 proceedings.
For questions concerning the code contact [email protected].
The different schemes' theoretical efficiencies have been calculated in the Mathematica notebook theo-efficiency.nb. It also contains the complete code deriving the optimal 4th order decomposition schemes with real and complex coefficients.
Simply follow the examples if you want to calculate the efficiency of your own decomposition scheme.
The coefficients required for a factorised implementation of Taylor and Chebyshev series are calculated in taylor_coefficients.nb.
The different schemes are implemented in C with an R front-end. The code is located in the simulation directory.
The implementation can easily be augmented by another decomposition (see ising_trotter.c) and the Hamiltonian can be exchanged (see ising_hamiltonian.c) without any need to modify the Trotterizations.
You might have to update the path to your R/include library in the Makefile. Find the path by executing Sys.getenv("R_INCLUDE_DIR") in your R environment.
After adjusting the Makefile according to your needs (possibly switching to another compiler), simply type make to compile all the C files.
The only high-level function noisy_trace calculates a trace (e.g. needed for the Frobenius norm) and can be executed by running source("ising_dos.R") in an R environment and then simply calling it.
The data used in the paper can be reproduced with the help of the benchmark.R script (e.g. run with Rscript benchmark.R in the console). Per default it is compiled without parallelisation and can take about an hour to run.
The data produced for the paper is located in simulation/benchmark.
The plots in the paper have been produced with gnuplot. The corresponding script plot_tex.gp can be found in simulation/benchmark as well.
v1.0.0 initial publication with the preprint, compatible with arXiv versions v1, v2, v3.
v1.1.0 added implementations of Yoshida's and Morales's methods, compatible with journal article and arXiv version v4.
v1.2.0 added factorised polynomial implementations, compatible with LATTICE 2023 proceedings.