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Data and Code for: Spectroscopic signatures of emergent elementary excitations in a kinetically constrained long-range interacting two-dimensional spin system

Tobias Kaltenmark, Chris Nill, Christian Groß, Igor Lesanovsky

Published Nov 17, 2025• 0 citations
Publisher

Abstract

Data for: Spectroscopic signatures of emergent elementary excitations in a kinetically constrained long-range interacting two-dimensional spin system Function of python scripts in this folder: Fig 2: corr_reduced.py: creates data for correlations in reduced model (V_1=50Omega) and saves it in data_reduced folder. Additionally, gives a plot with the corresponding correlations. corr_exact.py: creates data for correlations in the exact model (for V_1=1Omega and V_1=50Omega) and saves data in data_exact/V_1-1_Omega and data_exact/V_1-50_Omega. Additionally, gives a plot with the corresponding correlations. Fig_2.py: Creates Fig 2. from the data of the reduced (data_reduced) and exact (data_exact) model. Saves figures in 002_Figures (SVG and PDF) Fig 3: exact_spectroscopy.py: creates data for exact model spectroscopy with variable lattice size (maximally 3x3), Omega, Omega_rf. Here, one uses automatically VdW interactions V_2=V_1/8 and V_3=V_1/64. Saves data in same folder, which then has to be placed into the correct data folder data_NxN/exact/ M_E-N.py: creates data for resonant matrix element M_E for different variable lattice sizes (maximally 20x20) and saves data in corresponding folder. Additionally, gives plot of the data. reduced_spectroscopy.py: creates spectrum data for M_E dependent on adjustable lattice size. Saves data in same folder, which then has to be placed into the correct data folder data_NxN/reduced/ Fig_3.py: extracts data from corresponding folders and creates Fig 3, and saves it in 002_Figures (SVG and PDF). This is without the manually added inset in panel (a) of the level spectra. Fig B1: 2-fac_time_resolved.py: creates data of time-resolved spectrum for 2 atoms under facilitation and saves it in data folder. Additionally, gives plot of the data. Fig_B1.py: extracts data from corresponding folder and creates Fig B1, and saves it in 002_Figures (SVG and PDF). Contact: [Tobias Kaltenmark](mailto:tobias.kaltenmark@student.uni-tuebingen.de)

DOI
10.5281/zenodo.17629915

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Overview of data provided in support of Towards near-term quantum simulation of materials Contents of this folder: `analyse_materials_results.py`: script used to generate the summary tables and figures presented in the manuscript. `towards_quantum_simulation_data`: raw data used and produced when studying various 3D materials. `towards_quantum_simulation_analysis`: tables (in `.tex` format) and figures (as PDFs) presented in the manuscript. The contents of `towards_quantum_simulation_analysis` were generated by `analyse_materials_results.py`, i.e. the user need not run the script to produce the output files. Users can generate these analyses directly by running ```python analyse_materials_results.py```, though note the following packages will first need to be installed: `pandas >= 1.2.3` `numpy >= 1.23` `seaborn >= 0.11.1` `lfig >= 0.1.3` `matplotlib > 3.7.0` Included data Within `towards_quantum_simulation_data`, there are subfolders for each of the materials described in the manuscript, i.e. `SrVO3`, `GaAs`, `H3S`, `Si`, `Li2CuO2`. Within each material's folder are further subfolders for the `hamiltonian` and `encoding` used to represent the material, as well as subfolders for each of the `algorithms` studied. `hamiltonian`: files which specify the Hamiltonian for the material under study. There are a number of files `interactions.json` Hamiltonian terms in terms of Majorana monomials. `map_majorana_to_mode.json` keys are Majorana indices; values are the mode index to which they are associated. `map_mode_to_group.json` keys are mode indices; values are the group (or site) index to which they are associated. `map_group_to_position.json` keys are group indices; values are the corresponding 3D Cartesian coordinates of the lattice used to represent the material. `stage_data.json` contains key/value pairs of any other fields of interest. `encoding` files which specify the fermionic encoding which is customised for the material under study. `encoding.json` which details the edges of the hybrid compact encoding described in Section VI of the supplementary material. `precompiler.json` contains all the information which permits the encoding construction, including the Hamiltonian terms (`_interactions`) which match those in `hamiltonian/interactions.json`. The same mappings as present in the Hamiltonian data(a.g. `map_group_to_position`). `stage_data.json` contains key/value pairs of any other fields of interest. `algorithms` contains subfolders for each of the algorithms desribed in the manuscript Those explored for circuits depths: `TDSSplitTermsPriorityCircuitDepth` (TDS in the manuscript) `TDSSplitTermsPriorityCircuitDepthNoSwapNetwork` (TDS\*) `VQESplitTerms` (VQE) `VQESplitTermsNoSwapNetwork` (VQE*) each of which contain the files, inside the `circuitry` folder: `circuit_terms.csv`, which lists each individual term, together with their Pauli string and rotation angle, required to construct the corresponding quantum circuit `circuit_layers_to_implement.csv` groups the same terms into layers to achieve parallelism in the circuit. `stage_data.json` contains key/value pairs of any other fields of interest. and those used to compose measurement layers, as outlined in Section VII D of the supplementary material: `MeasurementCommutativity` `MeasurementNaiveQubitwise` `MeasurementNonCrossing` each of which contain the files, inside the `compilation` folder: `layers.csv` lists the terms which may be measured simultaneously to achieve the measurement strategies shown in Table S14. `stage_data.json` contains key/value pairs of any other fields of interest. CSV files In `towards_quantum_simulation_data`, there are unified CSV files containing the results of applying the procedures described in the manuscript to the target materials. `circuit_costs.csv`: results of running the circuit compiler described in the manuscript. `measurements.csv`: results of running the measurement compiler described in the manuscript. These CSVs are used in the analysis script `analyse_materials_results.py` to produce the figures and tables presented in the manuscript.
This archive contains the numerical data and scripts used to generate the figures for the paper “Energy-selective quantum search with Ising Hamiltonian phase oracles”. The main numerical dataset is used for the scaling analysis of the correlation-induced resonance displacement φ₀ in the zero-field random Ising ensemble. The simulations use dimensionless units with σ_J = 1 and the Hamiltonian H(s) = 2 sum_{i<j} J_ij s_i s_j, where the couplings are independent Gaussian random variables, J_ij ~ N(0, 1), and h_i = 0. For each random Ising instance, the archive stores the truncated characteristic-function coefficients g_m = 2^{-n} Tr exp(-i m T H), m = 0, ..., 15. These coefficients are used to extract the local displacement φ₀ from the zero of the imaginary part of the response function C(φ) = 2 sum_{m=0}^{15} g_m (-1)^m exp(i m φ) - 1. The quantity plotted in the paper is the disorder-averaged second moment <φ₀²> and the scaled combination n⁶<φ₀²>. The Monte Carlo average is over independent disorder realizations only. For each realization, the trace over spin configurations is evaluated deterministically. The data cover even system sizes n = 18, 20, 22, ..., 36. For the largest systems, the computation splits the spins into two equal halves, performs GPU block contractions, and uses the zero-field spin-flip symmetry H(s)=H(-s) to reduce the sum by a factor of two. Archive contents - scripts/01_generate_phi0_coefficients.py Generates the characteristic-function coefficient files g_m for the random Ising ensemble. - scripts/02_analyze_phi0_scaling.py Computes φ₀, bootstrap confidence intervals, the finite-n covariance-sum comparison, and the scaling plots. - scripts/03_make_gaussian_amplification.py Generates the Gaussian amplification figure used as Fig. 1 in the paper. - data/phi0_coefficients/ Directory for the NumPy .npz files containing the characteristic-function coefficients. The production files have names of the form Nq_<n>_K_<K>.npz. The .npz files are saved without pickle objects. They can be read with standard NumPy using np.load. Typical usage To regenerate the Gaussian amplification figure: python scripts/03_make_gaussian_amplification.py --output-dir output/fig1_gaussian To analyze the φ₀ scaling data: python scripts/02_analyze_phi0_scaling.py \ --data-dir data/phi0_coefficients \ --output-dir output/phi0_scaling To run a short test calculation of the characteristic-function coefficients: python scripts/01_generate_phi0_coefficients.py \ --smoke-test \ --output-dir output/smoke_test_coefficients To regenerate the full production dataset on a CUDA-capable GPU: python scripts/01_generate_phi0_coefficients.py \ --production \ --output-dir data/phi0_coefficients The production calculations were performed using CuPy on an NVIDIA GPU. The analysis and plotting scripts use NumPy, pandas, and Matplotlib.
This repository provides the figure data and numerical simulation codes supplement to the manuscript “Dynamical freezing and enhanced magnetometry in an interacting spin ensemble” (arXiv:2507.22982). Contents:--Main_text_figures--Extended_Data_figures Each folder contains the numerical or experimental data used to generate the corresponding figures in the manuscript. All figures can be reproduced by straightforward plotting of the included .csv files. A short description of each dataset is provided within the file headers. --Exact_diagonalization_code--Discrete_truncated_Wigner_approximation_code These directories contain the codes used in the numerical simulations presented in the paper. Each code package includes a detailed README file explaining the workflow, parameters, and usage.
File listing Data_Figures folder: contains data relating to figure in the main text The source data is available in the corresponding folder. For each panel, there are files named as "fig{figure number}{panel label}_{description}.mat". The following is a description of the variable names in each file. Independent *********** tlist: interaction time, t (ns) freq: frequency domain of FFT, \omega/2\pi (MHz) Dependent ********* imbalance: the imbalance fidelity: the four qubit fidelity entropy: the fout-qubit entropy fourier: the absolute value of Fourier transformation amplitude of imbalance suffix ****** _exp: experimental result _simu: numerical result