Results from "Adaptive Encoding Strategy for Quantum Annealing in Mixed-Variable Engineering Optimization"

This repository contains the data supporting the publication "Adaptive Encoding Strategy for Quantum Annealing in Mixed-Variable Engineering Optimization."

Context and methodology

This dataset originates from computational engineering optimization, specifically mixed discrete–continuous structural design, using quantum annealing (QA). Its purpose is to quantify how the binary budget per continuous variable (N) in fixed encodings affects solution accuracy on hardware-embedded QA and to evaluate the proposed adaptive encoding that updates representable ranges during optimization.

In the empirical error analysis, we consider an illustrative fluid-structure-interaction problem to measure the relative H^1 error (median and interquartile ranges (IQRs)) in the structure's displacement as a function of $N$ and report chain-break statistics, showing that QA accuracy improves only up to moderate bit depths before plateauing. In contrast, the adaptive encoding exhibits a monotonic decrease in error across coupling iterations, achieving a much lower final error with the same binary budget.

For a structural design optimization benchmark, we integrate the adaptive encoding into a quadratic penalty method, updating ranges of continuous force variables at each iteration; we compare solution accuracy for the adaptive encoding with reference results from the literature (fixed encoding) and perform parameter studies over the relaxation factor for range updates, the initial range scale, and the number of QA reads, reporting relative H^1 error trajectories (median and IQRs) across penalty iterations.

Technical details

Structure of the dataset

The dataset is organized according to the structure of the publication:

• 3.1 Empirical Error Analysis
• 3.2 Structural Design Optimization with Adaptive Encoding Strategy
  • 3.2.1 Effect of the Range Relaxation Factor in the Adaptive Encoding
  • 3.2.2 Sensitivity to Initial Ranges
  • 3.2.3 Impact of Suboptimal Solutions

Each subsection (3.1 and 3.2) has its own top-level folder. Within the folder for subsection 3.2, there are subfolders for each subsubsection (3.2.1, 3.2.2, and 3.2.3). We detail the different datasets below (see Further details).

All numerical data are stored as CSV files. Unless noted otherwise, column names follow these conventions: N (number of binary variables per continuous variable), iteration (iteration index of the coupling or penalty method), error (relative H^1 error), error_ba (best-approximation/encoding‑optimal error), and chain_break (chain break fraction). Nodal solution values with their range limits are reported per node, using a suffix indicating the node index, for example, node_0_min or node_1_max. When results for both encodings appear in the same file, columns use the suffixes fixed and adaptive (e.g., error_fixed, error_adaptive). For aggregated statistics, additional suffixes median, min, max, q25, and q75 indicate the median, minimum, maximum, and the 25th/75th percentile (IQR bounds), respectively.

Naming Convention

Top-level folder names mirror the corresponding subsection titles. Subfolders are named after the parameters varied in each study (e.g., relaxation_factor for the relaxation factor). Filenames describe their contents (e.g., error_over_iterations_....csv for errors over iterations) and include the suffix aggregated when they contain aggregated statistics across multiple runs.

Required software

No specialized software is required to open the files; any CSV-capable tool is sufficient.

Example usage with Python (pandas)

import pandas as pd
df = pd.read_csv("empirical_error_analysis/num_binary_variables/error_over_num_binary_variables_aggregated.csv")
print(df.head())

Licenses

Data is licensed under Creative Commons Attribution 4.0 International.

Funding

Further details

3.1 Empirical Error Analysis

In the following, we consider the relative H^1 error in the structure's displacement field.

Error for different numbers of binary variables in the fixed encoding

• Path: empirical_error_analysis/error_over_num_binary_variables_aggregated.csv
• Content: aggregated relative H1 error statistics (over 10 independent runs) versus the number of binary variables per continuous variable and chain break statistics

Error comparison of the fixed and the adaptive encoding during coupling iterations

• Path: empirical_error_analysis/error_over_iterations_aggregated.csv
• Content: aggregated relative H1 error statistics (over 10 independent runs) versus coupling iterations for $N=8$, comparing fixed and adaptive encodings

3.2 Structural Design Optimization with Adaptive Encoding Strategy

History of adaptive range limits

• Path: structural_design_optimization/range_limits_over_iterations.csv
• Content: the evolving representable ranges (min and max) of the continuous variables per iteration under the adaptive encoding

In the following, we consider the relative H^1 error in the structure's internal force field.

Error over quadratic penalty iterations  compared to the reference from the literature

• Path: structural_design_optimization/error_over_iterations.csv
• Content: error history over iterations (single run), including encoding-optimal errors (best approximation)

3.2.1 Effect of the Range Relaxation Factor in the Adaptive Encoding

Error over quadratic penalty iterations for different relaxation factors

• Path: structural_design_optimization/relaxation_factor/error_over_iterations_aggregated_<relaxation factor>.csv with relaxation factor in {0_25,0_5,0_75}for 0.25, 0.5, or 0.75, respectively.
• Content: aggregated relative H1 error statistics (over 10 independent runs) versus penalty iterations

3.2.2 Sensitivity to Initial Ranges

Error over quadratic penalty iterations for different initial ranges

• Path: structural_design_optimization/initial_range/error_over_iterations_aggregated_<initial range>.csv with initial range in {0_1,0_5,0_1}for [0,1], [0,5], or [0,10], respectively.
• Content: aggregated relative H1 error statistics (over 10 independent runs) versus penalty iterations

3.2.3 Impact of Suboptimal Solutions

Error over quadratic penalty iterations for different numbers of QA reads 

• Path: structural_design_optimization/num_reads/error_over_iterations_aggregated_<num reads>.csv with num reads in {400,800}for 400 or 800 reads, respectively.
• Content: aggregated relative H1 error statistics (over 10 independent runs) versus penalty iterations