Code - Robustness of Energy Landscape Control - Sensitivity vs RIM

SPDX-FileCopyrightText: Copyright (C) 2023-2024 Sean Patrick O'Neil seanonei@usc.edu
SPDX-FileCopyrightText: Copyright (C) 2023 Irtaza Khalid
SPDX-FileCopyrightText: Copyright (C) 2023-2024 SM Shermer lw1660@gmail.com
SPDX-FileCopyrightText: Copyright (C) 2023-2024 Frank C Langbein frank@langbein.org

SPDX-License-Identifier: CC-BY-SA-4.0

Recent achievements in quantum control have resulted in advanced techniques for designing controllers for applications in quantum communication, computing, and sensing. However, the susceptibility of such systems to noise and uncertainties necessitates robust controllers that perform effectively under uncertainty conditions to realize the full potential of quantum devices. The time-domain log-sensitivity and a recently introduced robustness infidelity measure (RIM) are two means to quantify controller robustness in quantum systems. The code and data in this data set allows for comparison between the log-sensitivity and RIM for controllers designed to achieve high-fidelity of excitation transfer in spin rings and chains. This code and data was originally developed for:

[1] S. P. O'Neil, et al., "Analyzing and Unifying Robustness Measures for Excitation Transfer Control in Spin Networks," in IEEE Control Systems Letters, vol. 7, pp. 1783-1788, 2023, [DOI:10.1109/LCSYS.2023.3279797] [arXiv:2303.09518] [PDF].

The results of running the code is available in the results submodule that can be cloned via git submodule update --init --recursive or directly at https://qyber.black/spinnet/results-robustness-of-energy-landscape-control-sensitivity-vs-rim/.

This repository is developed on qyber/black at https://qyber.black/spinnet/code-robustness-of-energy-landscape-control-sensitivity-vs-rim and is mirrored on github.

Versions

Version 1.0.0: initial release for the paper

Notation

The files and figures in this project use the following notation:

N   - size (number of spins) for a given ring or chain; takes values of 5 or 6
out - target spin for excitation transfer 
opt - optimizer/optimization condition descriptor
      for chains takes values in {lbgfs,ppo,nmplus,snob}
      for rings takes values in {fidelity,dephasing,overlap}
nl  - (noise level) size of the training noise for RIM data; takes values in [0.0,0.01,0.02,0.03,0.04,0.05,0.1] with default    
      value 0.1 

Data Description

The data intended for input to the computation and analysis code is saved in the data-raw directory. Upon downloading the code and data, this directory should be saved directly subordinate to the root directory. The established hierarchy uses the following sub-directories :

• controllers-chains - All controller data for chain problems is saved in this directory as a .csv file with columns 2 through N+1 containing the bias field values, column N+2 containing the read-out time, and column N+3 containing the nominal fidelity.
• controllers-rings - All controller data for ring problems is saved in this directory as a .csv file with the first N columns containing the bias fields values, column N+1 containing the read-out time, and column N+2 containing the nominal fidelity.
• dephasing_op - Each set of 10^6 dephasing operators for rings and chains of size N=5 and N=6 is saved as a .csv file in this directory. Each row of the file corresponds to one dephasing operator.
• rim-chains - Spreadsheet of RIM data for chain problems saved as tn_nl_opt_dephasing_rim_1s_trace_chain_N_out.csv.
• rim-rings - Spreadsheet of RIM data for ring problems saved as opt_dephasing_rim_1s_trace_ring_N_out.csv.

Computation and Analysis Code Description

The code to compute and analyze the data based on the inputs form the data-raw directory are located in the code-matlab directory. The code-matlab directory should be saved intact and directly subordiante to the root directory and all routines are designed to be run from the code-matlab directory.

Routine	Description
run_all_script.m	When run, this script calls on each routine below to compute and generate all results saved in the results directory. The routines are designed to create each necessary sub-directory within results.
convert_rnim_raw_data_to_mat_chains.m	Converts relevant RIM data from the .csv files in data-raw/rim-chains and saves as .mat files in results/rim-chains as rim_noise_nl_opt_N-chain_1-out.mat.
convert_rim_raw_data_to_mat_rings.m	Converts relevant RIM data from the .csv files in data-raw/rim-rings and saves as .mat files in results/rim-rings as rim_opt_N-ring_1-out.mat`.
convert_dop_data_all.m	Takes the .csv files for the dephasing processes from data-raw/dephasing_op and translates them into .mat files saved in results/dephasing_op as dephasingop_1d_ring-xx-N.mat. Data saved as a cell array of 100,000 upper triangular matrices. Calls on convert_dop.m and InvertDephasing.m.
convert_dop.m	Executes conversion of dephasing operators in .csv spreadsheet to an array for use with MATLAB routines.
InvertDephasing.m	Tests each dephasing operator for complete positivity.
convert_controller_data_to_mat_chains.m	Converts the controller data in data-raw/controllers-chains to usable .mat files and saves as noise_nl_opt_N-chain_1-out.mat in the results/controllers-chains directory. Calls on convert_controller.m.
convert_controller_data_to_mat_rings.m	Converts the controller data in data-raw/controllers-rings to usable .mat files and saves as opt_N-ring_1-out.mat in the results/controllers-rings directory. Calls on convert_controller.m.
convert_controller.m	Reads in .csv file from data-raw/controllers-{rings,chains} and converts data to a MATLAB structure.
calc_log_sens_chain.m	Computes the analytic log-sensitivity for chain problems and saves as log_sens_nl_opt_N-chain_1-out.mat in the results/log_sens-chains directory. Calls on bloch_basis.m.
calc_log_sens_chain_kde.m	Computes the KDE-based log-sensitivity for chain problems and saves as log_kde_nl_opt_N-chain_1-out.mat in the results/kde-chains directory. Calls on AnalyzeRobustnessDephasing.m and AnalyzeErrorDensity.m.
calc_log_sens_ring.m	Computes the analytic log-sensitivity for ring problems and saves as log_sens_opt_N-ring_1-out.mat in the results/log_sens-rings directory . Calls on bloch_basis.m.
calc_log_sens_ring_kde.m	Computes the KDE-based log-sensitivity for ring problems and saves as log_kde_opt_N-ring_1-out.mat in the results/kde-rings directory. Calls on AnalyzeRobustnessDephasing.m and AnalyzeErrorDensity.m.
bloch_basis.m	Computes basis matrices for computation of the analytic log-sensitivity.
AnalyzeRobustnessDephasing.m	Produces kernel of error values for input to KDE.
AnalyzeErrorDensity.m	Produces kernel density estimate of mean fidelity error.
calc_sens_vs_adjusted_rim.m	Computes the relative difference between the analytic differential sensitivity and the adjusted RIM for all ring and chain controllers and saves the result as results/sens_v_rim_sens.mat.
analyze_chains_composite.m	Computes correlation between analytic and KDE-based log-sensitivity versus RIM as well as the correlation between both log-sensitivity measures and RIM versus the nominal fidelity error and saves the results as results/corr-chain-noise_nl-log_sens-rim.csv and results/corr-chain-noise_nl-log_sens-rim-err.csv.
analyze_chains_composite_v2.m	Computes correlation between both differential sensitivity measures (analytic and KDE) versus RIM as well as the correlation between both sensitivity measures and RIM versus the nominal fidelity error and saves results as results/corr-chain-noise_nl_-sens-adj_rim.csv and results/corr-chain-noise_nl-sens-adj_rim-err.csv
analyze_rings_composite.m	Computes correlation between analytic and KDE-based log-sensitivity versus RIM as well as the correlation between both log-sensitivity measures and RIM versus the nominal fidelity error and saves the results as results/corr-ring-log_sens_rim.csv and results/corr-ring-log_sens-rim-err.csv.
analyze_rings_composite_v2.m	Computes correlation between both differential sensitivity measures (analytic and KDE) versus RIM as well as the correlation between both sensitivity measures and RIM versus the nominal fidelity error and saves results as results/corr-ring-sens_adj_rim.csv and results/corr-ring-sens-adj_rim-err.csv.

The python files to process the RIM results are in code-python and the dependencies can be installed via pip3 install -r code-python/requirements.txt. The files are:

File	Description
rim_vs_logsensitivity.py	RIM vs. log-sensitivity for chains and rings; creats the results/figures/rim_vs_logsensitivity-{rings,chains} plots.
generate_rims_heatmap.py	RIM heatmaps and correlations with log sensitivity; computes the rim_heat-{chains,rings} files in results/results and corresponding plots in results/figures/rim_heat-{chains,rings}.
plot_all_adj_rim_vs_kdtau.py	Plot Kendall taus for RIM vs. differential sensitivity.
rim_vs_diffsens_dists_chains.py	Kendall-tau between RIM and log sensitivity for chains (for plot_all_adj_rim_vs_kdtau.py).
rim_vs_diffsens_dists_rings.py	Kendall-tau between RIM and log sensitivity for rings (for plot_all_adj_rim_vs_kdtau.py).
dephasing_fid.py	Compute infidelities with dephasing operators.
noise_model.py	Perturbation models.
utilities.py	Helper functions.

Plot Routines

The following plot routines are designed to be run from the code-matlab directory following completion of the computation and analysis routines above.

Routine	Description
plot_all_script.m	This script executes all plot routines below and requires the user to input the noise_choice variable to select the proper RIM data.
plot_all_chain.m	Constructs plots of both log-sensitivity measures, RIM, and nominal fidelity error versus controller index saved as figures/composite-chains/comparison_nl_opt_N-chain_1-out.{fig.png} and scatter plots of both log-sensitivity measures and RIM versus nominal fidelity error saved as figures/composite-chains/scatter_nl_opt_N-chain_1-out.{fig,png}.
plot_all_chain_v2.m	Constructs plots of both sensitivity measures, adjusted RIM, and nominal fidelity error versus controller index saved as figures/composite-chains-v2/comparison_v2_nl_opt_N-chain_1-out.{fig.png} and scatter plots of both sensitivity measures and adjusted RIM versus nominal fidelity error saved as figures/composite-chains-v2/scatter_v2_nl_opt_N-chain_1-out.{fig,png}.
plot_all_ring.m	Constructs plots of both log-sensitivity measures, RIM, and nominal fidelity error versus controller index saved as figures/composite-rings/comparison_opt_N-ring_1-out.{fig.png} and scatter plots of log-sensitivity measures and RIM versus nominal fidelity error saved as figures/composite-rings/scatter_opt_N-ring_1-out.{fig,png}.
plot_all_ring_v2.m	Constructs plots of both sensitivity measures, adjusted RIM, and nominal fidelity error versus controller index saved as figures/composite-rings-v2/comparison_v2_opt_N-ring_1-out.{fig.png} and scatter plot of both sensitivity measures and adjusted RIM versus nominal fidelity error saved as figures/composite-rings-v2/scatter_v2_opt_N-ring_1-out.{fig,png}.
plot_all_heatmaps_chains.m	Produces a multi-pane figure with a heatmap of the fidelity error distribution, bias fields, initial density matrix, and density matrix at read-out time and saves as figures/heatmaps-chains/noise_nl_opt_N-chain_1-out_ctrl_#.{fig.png}. User may set number of controllers to plot in the routine under index variable. Calls on PlotHeatMaps.m.
plot_all_heatmaps_rings.m	Produces a multi-pane figure with a heatmap of the fidelity error distribution, bias fields, initial density matrix, and density matrix at read-out time and saves as figures/heatmaps-rings/opt_N-ring_1-out_ctrl_#.{fig.png}. User may set number of controllers to plot in the routine under index variable. Calls on PlotHeatMaps.m.
plot_all_rim_sens_heatmap_chains.m	Produces a heatmap of RIM for increasing perturbation strength versus the differential sensitivity and saves as figures/heat_maps/heat_map_chain_opt_N_out.{fig,png}.
plot_all_rim_sens_heatmap_rings.m	Produces a heatmap of RIM for increasing perturbation strength versus the differential sensitivity and saves as figures/heat_maps/heat_map_ring_opt_N_out.{fig,png}.
PlotHeatMaps.m	Routine that produces the heat map for plot_all_heatmaps_{ring/chains}.m.
heatmaptext.m	Helper script for producing heat maps called on by PlotHeatMaps.m.
Inferno.m	Helper script for coloring heat maps called on by PlotHeatMaps.m.