DOI: 10.5281/zenodo.11220877
title: Data for "Towards quantum gravity with neural networks: Solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit"

description: 1. Repository Information

This repository contains the data produced during the work discussed in in the paper "Towards quantum gravity with neural networks: Solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit". Please refer to this paper for more details on how the data was produced.

 

2. Citing

In addition to citing this repository, please also cite the paper mentioned above if you use the data. The citation is:

Hanno Sahlmann and Waleed Sherif 2024 Class. Quantum Grav. 41 215006

 

3. File Description

In this repository, you will find 4 general directories (here called parent directories):



Ground Energy + Fluctuations

Misc

Quantum Constraint

Volume


Each of these directories correposnd to different data produced and discussed in the corresponding parts in the paper mentioned above (e.g. the directory "Ground Energy + Fluctuations" contains the data used in Table 1 and Table 2 in the paper while the "Volume" directory contains the data used in Section 4.3 of the paper).

Some of these parent directories, which involve simulations solving constraints, contain within them several sub-directories (child directories) corresponding to different produced data. The raw data of the simulation can be found in a .json file inside the child directories.

 

4. Usage

4.1 Raw Simulation Data

The .json files include the raw data produced during the study. These files can be easily accessed using a python script, as an example, by using:

import json

filePath = ...

data = json.load(open(filePath))

where filePath should hold the correct path to the local data once downloaded. Once loaded, the data is handled as a python dict.

 

The dictionary will have at least one parent key called "Energy". The data in the "Energy" key corresponds to the data being minimised. The data in any other parent key correspond to operators which were being observed during the simulation. For example, in the data in the "Quantum Constraint" directory, some .json files will have multiple parent keys such as FG, H, HG, .... Each of these keys correspond to different operators which were observed during that simulation. Each parent key is yet another dictionary in itself. The structure of the dictionaries corresponding to any parent key are always the same and always include the keys:



iters

Mean

Variance

Sigma

R_hat

TauCorr


Hence, to access the "Mean" values, you use data["Energy"]["Mean"] (or alternatively data["FG"]["Mean"] if you wish to observe the value of the F + G operator during the simulation). The data represents the values during a simulation of typically 500 iterations, hence, each of the keys mentioned above will correspond to an array of 500 items. The iters array includes merely the iteration number. The Mean array includes the value of the expectation value of the constraint at the corresponding iteration. The Variance, Sigma, R_hat and TauCorr includes the values of the variance and error in the expectation value at the given iteration as well as the split R-hat diagnostic and the time correlation also in the given iteration. 

 

4.2 Variational State Data

The files for the variational arrays are too large to be uploaded to a general repository hosting service. Therefore, they will be provided directly upon request in a direct download link. Please contact the author of the paper (Waleed Sherif, email: waleed.sherif@fau.de) for accessing the data. 

 

4.3 Fluctuation results

In some child directories, there will be a .txt file which includes the output of the calculation of the expectation value of some operators and their quantum fluctuations. These are only results, and not data, as the data can only be computed during the simulation.

 

4.4 Probabilities

The "Misc/Probabilities" directory contains .npy files which should be handled in the same manner as the variational states. These files correspond to the probability simulations conducted in section 4.4.4 in the paper.

 

5. Contact

Shall you have any unanswered questions regarding the usage of the data, please contact the author:

Waleed Sherif

email: waleed.sherif@fau.de

 

6. References

The data provided in this repository was produced using the NetKet[1] package

[1] doi: 10.21468/SciPostPhysCodeb.7