wavefunction_branching

A package for identifying non-interfering "branch" decompositions of Matrix Product State wavefunctions, and then continuing time-evolution after sampling from the branches

Installation

In the terminal, cd into this repo then run make install or pip install -e .

Running time-evoution with branching

The main script for evolving and branching a wavefunction is located at wavefunction_branching/evolve_and_branch_finite.py

This script can be run using a bash command such as

python wavefunction_branching/evolve_and_branch_finite.py  --name=$name  --outfolder=$outfolder  --J=$J  --g=$g  --chi_max=$chi_max  --n_sites=$n_sites  --BC_MPS=$BC_MPS  --dt=$dt  --N_steps_per_output=$N_steps_per_output  --svd_min=$svd_min  --trunc_cut=$trunc_cut  --evo_method=$evo_method  --branching=$branching  --max_branches=$max_branches  --chi_to_branch=$chi_to_branch  --max_trace_distance=$max_trace_distance  --max_overlap_error=$max_overlap_error  --t_evo=$t_evo  --min_time_between_branching_attempts=$min_time_between_branching_attempts  --max_branching_attempts=$max_branching_attempts  --branch_function_name=$branch_function_name  --stop_before_branching=$stop_before_branching  --maxiter_heuristic=$maxiter_heuristic  --tolEntropy=$tolEntropy  --tolNegativity=$tolNegativity  --seed=$seed  2>&1 | tee $outfolder/out-$date-$name.txt

This will produce plots of expectation values, as well as pickle files, stored in outfolder.

Alternatively, you can run ./make_sbatch_files.py to generate a series of bash files in a runs folder. These bash files run simulations reproducing the results of our paper.

Analysing results of branching time-evolutions

Then, once multiple runs are complete, you can compare them with two scripts: evolution_analysis/pickle_analysis.py and evolution_analysis/error_analysis.py. These should be run one after another. The former opens the resulting pickle files matching a pattern, and compiles a dataframe of expectation values and errors over time. The latter should be run after the former, and it plots the errors from the ground-truth in the Ising model.

Branch decomposition functions

The branching evolution script can use one of many algorithms for performing the branch decompositions. To see which branching functions are implemented, check the iterative_method and graddesc_method variables of the branch() and branch_from_theta() functions in wavefunction_branching/decompositions/decompositions.py

    iterative_method: None
    | Literal[
        "bell_discard_classical",
        "bell_keep_classical",
        "vertical_svd_micro_bsvd",
        "pulling_through",
    ],
    graddesc_method: None
    | Literal[
        "rho_LM_MR_trace_norm_discard_classical_identical_blocks",
        "rho_LM_MR_trace_norm_identical_blocks",
        "rho_LM_MR_trace_norm",
        # "rho_half_LM_MR_trace_norm",
        "graddesc_global_reconstruction_non_interfering",
        "graddesc_global_reconstruction_split_non_interfering",
    ],

These branch functions are defined in wavefunction_branching/decompositions.

Benchmarking branch decomposition functions

Code for benchmarking the branch functions (without needing to run a full evolution) is in instantaneous_benchmarks. There are three relevant files, which should be run in order:

1. instantaneous_benchmarks/generate_test_inputs.py Which generates various inupt tensors to test the decomposition method on
2. instantaneous_benchmarks/benchmark_decompositions.py Which performs benchmarks on the methods defined within `get_blockdiag_methods()'
3. instantaneous_benchmarks/plot_benchmarks.py Which plots the results of the benchmarks.