Data for "Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity"

1. Repository Information This repository contains numerical data produced for the paper "Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity". Please refer to the paper for more details on the physical setting, ansatz choices, optimisation procedure, and interpretation of the results. Two classes of neural ansatz data are included: - MLP ansatz simulations.- Structured ansatz simulations. For each available spin cutoff, the repository provides: - the raw simulation log in JSON format, and- the trained final variational state/network in MPACK format. The main purpose of the data is to provide the simulation logs and trained states underlying the near-kernel solutions analysed in the paper, including the states used in the coherent-state and near-kernel diagnostics. Hydra-based reproducible neuraLQX simulations are available at https://github.com/waleed-sh/qrlg-vmc. These reproducible workflows also generate the plots shown in the paper. 2. Citing If you use this data, please cite this repository and the corresponding paper: Ilkka Mäkinen, Hanno Sahlmann and Waleed Sherif, "Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity", arXiv:2605.18625 [gr-qc], 2026. 3. File Description The repository is organised by ansatz class and charge cutoff. The main data directory is: DATA/ Inside it, there are three ansatz directories: DATA/CORRELATED/DATA/MLP/DATA/STRUCTURED/ The `DATA/CORRELATED/` directory contains the correlated-state ansatz simulation at the following charge cutoff: cutoff_25p0/ The `DATA/MLP/` directory contains MLP ansatz simulations at the following charge cutoffs: cutoff_20p0/cutoff_25p0/cutoff_50p0/cutoff_100p0/cutoff_150p0/cutoff_200p0/cutoff_250p0/cutoff_300p0/cutoff_350p0/cutoff_400p0/ The `DATA/STRUCTURED/` directory contains structured ansatz simulations at the following charge cutoffs: cutoff_20p0/cutoff_25p0/cutoff_50p0/cutoff_100p0/cutoff_150p0/cutoff_200p0/cutoff_250p0/cutoff_300p0/cutoff_350p0/cutoff_400p0/cutoff_450p0/cutoff_500p0/ NOTE: The cutoff directory name encodes (almost) the half of the spin truncation. For example, cutoff_250p0/ corresponds to j_max = 501.0 where `p` denotes the decimal point in the folder name. Inside each cutoff directory there is a `simulation/` directory: DATA/MLP/cutoff_250p0/simulation/DATA/STRUCTURED/cutoff_250p0/simulation/ Each `simulation/` directory contains two files: *_LogData_*.json*_SerialisedState_*_FinalState.mpack The `*_LogData_*.json` file contains the raw logged quantities recorded during the variational Monte Carlo optimisation. The `*_SerialisedState_*_FinalState.mpack` file contains the serialised final trained variational state/network obtained at the end of the simulation. Only final trained states are included in this curated data directory. Aborted intermediate states are not included. 4. Usage 4.1 Loading the JSON Files The `.json` files contain the raw logged quantities recorded during the variational optimisation. They can be loaded in Python using the standard `json` module: import json file_path = "DATA/MLP/cutoff_250p0/simulation/path_to_log_file.json" with open(file_path, "r") as f: data = json.load(f) After loading, `data` is a Python dictionary. 4.2 JSON File Structure Each JSON file is a nested dictionary. The top-level entries are the logged quantities from the optimisation. In the files included here, typical top-level keys are: acceptanceConstraint The `acceptance` entry stores the Metropolis acceptance history: data["acceptance"] = { "iters": [...], "value": [...]} The `Constraint` entry stores the Monte Carlo estimates of the quadratic constraint during optimisation: data["Constraint"] = { "iters": [...], "Mean": { "real": [...], "imag": [...] }, "Variance": [...], "Sigma": [...], "R_hat": [...], "TauCorr": [...]} 4.3 Meaning of the JSON Keys For each logged quantity, the internal keys have the following meaning. `iters` The iteration numbers of the variational optimisation. `value` The logged scalar value at each optimisation iteration. This is used, for example, for the `acceptance` history. `Mean` The Monte Carlo estimate of the expectation value of the logged quantity at each iteration. Since the expectation value may be complex, it is stored with separate real and imaginary parts: data["Constraint"]["Mean"]["real"]data["Constraint"]["Mean"]["imag"] `Variance` The estimated variance of the logged quantity at each iteration. `Sigma` The estimated statistical error of the Monte Carlo estimate at each iteration. `R_hat` The split R_hat diagnostic at each iteration. This is used as a convergence diagnostic for the Monte Carlo chains. `TauCorr` The estimated autocorrelation time at each iteration. 4.4 Accessing Data Entries To access the iteration numbers for the constraint, use: data["Constraint"]["iters"] To access the real part of the mean constraint value, use: data["Constraint"]["Mean"]["real"] To access the imaginary part of the mean constraint value, use: data["Constraint"]["Mean"]["imag"] To access the variance, statistical error, split R_hat, and autocorrelation time, use: data["Constraint"]["Variance"]data["Constraint"]["Sigma"]data["Constraint"]["R_hat"]data["Constraint"]["TauCorr"] To access the Metropolis acceptance history, use: data["acceptance"]["iters"]data["acceptance"]["value"] 4.5 Array Lengths Each array stores the value of the corresponding quantity over the course of the variational optimisation. For example, if a simulation contains 1000 iterations, then the following arrays will typically each contain 1000 entries: data["Constraint"]["iters"]data["Constraint"]["Mean"]["real"]data["Constraint"]["Mean"]["imag"]data["Constraint"]["Variance"]data["Constraint"]["Sigma"]data["Constraint"]["R_hat"]data["Constraint"]["TauCorr"] Some JSON files may contain `null` entries. When loaded in Python, these become `None`. These should be handled appropriately when plotting or post-processing the data. 4.6 Example: Plotting the Constraint The following example plots the real part of the mean constraint value over the optimisation iterations: import json import matplotlib.pyplot as plt file_path = "DATA/MLP/cutoff_250p0/simulation/path_to_log_file.json" with open(file_path, "r") as f: data = json.load(f) iters = data["Constraint"]["iters"] constraint_real = data["Constraint"]["Mean"]["real"] plt.plot(iters, constraint_real) plt.xlabel("Iteration") plt.ylabel("Re <Constraint>") plt.show() Similarly, the statistical error can be plotted using: sigma = data["Constraint"]["Sigma"] or used as error bars in a plot. 4.7 Loading the MPACK Files The `.mpack` files are serialised trained variational states/networks. They are not plain-text files. They should be loaded using the compatible neuraLQX serialisation utilities associated with the simulation code. The reproducible Hydra-based simulation and post-processing workflows are available at: https://github.com/waleed-sh/qrlg-vmc These workflows reproduce the simulations and generate the plots shown in the paper. 5. Contact If you have any questions regarding the usage of the data, please contact the corresponding author: Waleed Sherif email: [e-mail] 6. References The data provided in this repository was produced using neuraLQX, which is built on NetKet. [1] neuraLQX, GitHub: [https://github.com/waleed-sh/neuraLQX] [2] Reproducible Hydra-based simulations for this paper: [https://github.com/waleed-sh/qrlg-vmc] [3] NetKet: doi: 10.21468/SciPostPhysCodeb.7 doi: 10.1016/j.softx.2019.100311