Quantum-Inspired Optimization Process for Data Imputation

arXiv:2505.04841 · quant-ph, cs.AI · Submitted 2025-05-07 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Hi, I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Quantum-Inspired Optimization Process for Data Imputation".

Mira: Here's the gist of the paper. The gist Data imputation is a critical step in data preprocessing, particularly for datasets with missing or unreliable values, and this study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset which contains biologically implausible missing values across several clinical features Novel Methodology The proposed framework integrates Principal Component Analysis (PCA) with quantum-assisted rotations to reconstruct missing values while preserving statistical fidelity The method begins by imputing missing values in the dataset using a measure of central tendency, such as mean, median, or mode PCA is then applied to reduce the dimensionality of the dataset by identifying directions that maximize variance through eigenvalue decomposition These components are subjected to quantum-assisted rotations, optimized through a systematic process, to generate rotated versions of the principal components A key feature of this method is the enforcement of statistical bounds, ensuring that reconstructed values remain within ±2 standard deviations (SD) of the original data distribution Optimization and Constraints To enhance computational efficiency and robustness, the framework evaluates multiple classical optimization techniques, including COBYLA, Differential Evolution, and Simulated Annealing The optimal rotation angles are obtained by minimizing a cost function defined as J(θ) = Xn i=1 X d j=1 Penalty Term + Deviation The optimization process is performed using classical optimizers such as Differential Evolution, COBYLA, and Annealing A penalty mechanism is integrated to discourage values from clustering excessively around the imputed central tendency measure This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov–Smirnov test pvalues between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE 0.99 in classical methods such as Mean, KNN, and MICE.> Experimental Validation The study was conducted on the UCI Diabetes dataset, where six variables exhibiting biologically implausible zero values were chosen for imputation The KS test observations indicate that quantum-based imputation methods produce significantly lower KS test p-values for features such as SkinThickness, Insulin, BMI, and DiabetesPedigreeFunction Classical methods exhibit minimal Wasserstein distances (all zeros), suggesting that they do not introduce significant changes compared to the original dataset The findings highlight that the proposed framework enhances reliability in complex datasets by ensuring reconstructed values align more closely with real-world statistical distributions The method successfully diversifies imputed features, redistributing values that were previously concentrated at the mean to exhibit a spread that aligns with natural variability The framework is designed to be computationally scalable and provides a robust solution for imputation tasks in domains such as healthcare and AI pipelines This forward-thinking design positions the method as a promising candidate for future breakthroughs in quantum-enhanced data imputation The final dataset is generated by averaging the values from the three rotated datasets for each imputed feature This pipeline offers a novel approach to handling missing data by integrating statistical imputation, quantum-enhanced transformations, and gradient-free optimization The authors are grateful to the IBM Quantum Experience platform and their team for developing the Qiskit platform and providing open access to their simulators for running quantum circuits and performing the experiments reported here Page 1 --- The gist Data imputation is a critical step in data preprocessing, particularly for datasets with missing or unreliable values, and this study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset which contains biologically implausible missing values across several clinical features Quantum-Inspired Optimization Process for Data Imputation The method integrates Principal Component Analysis (PCA) with quantum-assisted rotations to reconstruct missing values while preserving statistical fidelity This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov–Smirnov test pvalues between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE 0.99 in classical methods such as Mean, KNN, and MICE.> The imputation process unfolds as follows<ref:2505.04841.

Paper summary: Kai: We started by looking at the paper "Quantum-Inspired Optimization Process for Data Imputation" and it lays out the thesis right away. The main point is that they introduce a novel framework which combines Principal Component Analysis, or PCA, with quantum-assisted rotations to reconstruct missing values while trying to maintain statistical fidelity.

Mira: They argue that conventional techniques often fail because they just produce imputations that are either too smooth or biased, so this quantum-inspired approach aims for statistically diverse and more representative imputations. The method starts by imputing the missing values using a measure of central tendency, like the mean or mode.

Lev: Before we get into the mechanics, just to frame it properly for real hardware, they show a schematic diagram illustrating the overall process of imputation where mu equals one Pn i is x i is the mean vector of X. Centering ensures that each feature has a mean of zero, which simplifies variance and covariance computations.

Kai: And after centering things, they apply PCA to reduce the dimensionality by finding directions that maximize variance through eigenvalue decomposition on the covariance matrix C. These principal components are then subjected to quantum-assisted rotations optimized through a systematic process.

Mira: The key part is that these rotated components are reconstructed back into the original feature space, and their averaged values replace the initial central tendency imputations. They also enforce statistical bounds during reconstruction, making sure the imputed values stay within plus or minus two standard deviations of the original data distribution.

Lev: That enforcement of statistical bounds is crucial because it’s what keeps us grounded in reality; without that constraint, you could end up with wildly unrealistic reconstructions that don't reflect any real clinical observation.

Kai: Then they discuss how they optimize those quantum-assisted rotations using classical gradient-free optimizers—specifically COBYLA, Simulated Annealing, and Differential Evolution—to generate the best possible angles for those rotations.

Mira: They evaluate these classical optimizers systematically to find the optimal rotation angles by minimizing a cost function defined as J(theta) which includes a penalty term and the deviation from the original data. This systematic search is how they claim they get robust results.

Lev: From an engineering standpoint, that means we're looking at a pipeline where classical optimization runs on top of the quantum transformation to find the parameters, which tells us exactly where the computational bottlenecks might lie if you try to run this on actual superconducting qubits.

Kai: So, in short, the paper claims this framework achieves statistically diverse and more representative imputations by using quantum-assisted rotations optimized via classical gradient-free optimizers while maintaining strict statistical bounds. This is the essence of their proposed method in "Quantum-Inspired Optimization Process for Data Imputation".

Mira: It matters because they show substantial improvements in distributional fidelity, such as an average reduction of over eighty-five percent in Wasserstein distance and a significant jump in Kolmogorov–Smirnov test p-values compared to classical methods like Mean or KNN.

Lev: That jump from p-values greater than zero point nine nine down to between zero point one eight and zero point two two is the concrete evidence they use to show that this approach is statistically sound and not just getting lucky with the numbers; it’s a genuine statistical improvement over simpler methods.

Kai: It really highlights that the combination of PCA, quantum rotation, and careful optimization isn't just some theoretical exercise; it yields imputations that are closer to what we expect from real-world biological data.

Conclusion: Kai: So wrapping up the discussion on "Quantum-Inspired Optimization Process for Data Imputation", the title and authors suggest this is a method about using quantum concepts to enhance classical data imputation techniques, specifically focusing on making those imputed values statistically sound.

Mira: What this means in simpler terms is that they developed a way to fill in missing data that doesn't just guess a number close to the mean, but actively works to make the imputed values spread out in a way that matches the real variability of the data.

Lev: It’s about taking the structure of PCA and injecting some quantum-inspired transformations into it, and then using classical optimization tools like COBYLA or Differential Evolution to fine-tune those transformations until they hit a statistical sweet spot defined by those bounds.

Kai: The implication for us in the world of AI pipelines is that this provides a statistically grounded and scalable strategy for imputation, especially in complex domains like healthcare where data quality is often a real issue.

Mira: It’s forward-thinking design because they've built something that can be mapped onto future quantum hardware as it matures, meaning the underlying structure is sound even if we aren't running the full quantum circuit yet.

Lev: The limitation they explicitly state is that they are relying on classical gradient-free optimizers to find those rotation angles, so for real hardware deployment, you’ll need a way to replace that search process with something more native to quantum computation.

Kai: So the final picture is that this work supports using optimization-guided rotations as a statistically grounded strategy for realistic imputation in healthcare and general AI pipelines by ensuring the imputed data aligns better with real-world statistical distributions.

Nishikanta Mohanty, Bikash K. Behera, Badshah Mukherjee, Christopher Ferrie

Centre for Quantum Software and Information, University of Technology Sydney · Bikas’s Quantum (OPC) Pvt. Ltd. · SAS Middle East Fz-Llc

quant-ph, cs.AI

Submitted: 2025-05-07

Updated: 2026-10-21

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 72/100

The gist: The gist Data imputation is a critical step in data preprocessing, particularly for datasets with missing or unreliable values, and this study introduces a novel quantum-inspired imputation framework

Key concepts

Principal Component Analysis (PCA): PCA is a technique used to reduce the dimensionality of data by finding new axes, or components, that capture the most variance in the dataset. It helps simplify complex data while retaining most of its important information. In this paper, PCA is used as a starting point before applying quantum rotations to improve feature reconstruction.
Quantum Rotation-Based Reconstruction: This involves applying specific rotations to the principal components derived from PCA using quantum-inspired methods. These rotations are optimized through classical algorithms like Simulated Annealing to generate transformed versions of the components. This process helps in reconstructing missing values in a way that respects the underlying data distribution.
Distributional Fidelity (Wasserstein W1): This measures how closely the imputed data distribution matches the original observed data distribution. A lower Wasserstein distance indicates better fidelity. The paper shows that quantum-inspired methods achieve substantially lower Wasserstein distances, meaning the reconstructed values are statistically closer to how they naturally occur in the real dataset.
Gradient-Free Optimization: These are mathematical techniques used to find the best parameters (in this case, rotation angles) without needing derivatives. Methods like Simulated Annealing and COBYLA are employed here. They systematically search for the optimal rotation angles that minimize a defined cost function, ensuring robust and efficient tuning of the imputation process.

Terminology

Clustering — 1× in this paper · explained in 2 episodes
Fidelity — 1× in this paper · explained in 2 episodes
Principal Component Analysis (PCA) — 1× in this paper · explained in 6 episodes
Wasserstein Distance — 1× in this paper · explained in 5 episodes

Summary

The gist Data imputation is a critical step in data preprocessing, particularly for datasets with missing or unreliable values, and this study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset which contains biologically implausible missing values across several clinical features

Novel Methodology

The proposed framework integrates Principal Component Analysis (PCA) with quantum-assisted rotations to reconstruct missing values while preserving statistical fidelity The method begins by imputing missing values in the dataset using a measure of central tendency, such as mean, median, or mode PCA is then applied to reduce the dimensionality of the dataset by identifying directions that maximize variance through eigenvalue decomposition These components are subjected to quantum-assisted rotations, optimized through a systematic process, to generate rotated versions of the principal components A key feature of this method is the enforcement of statistical bounds, ensuring that reconstructed values remain within ±2 standard deviations (SD) of the original data distribution

Optimization and Constraints

To enhance computational efficiency and robustness, the framework evaluates multiple classical optimization techniques, including COBYLA, Differential Evolution, and Simulated Annealing The optimal rotation angles are obtained by minimizing a cost function defined as J(θ) = Xn i=1 X d j=1 Penalty Term + Deviation The optimization process is performed using classical optimizers such as Differential Evolution, COBYLA, and Annealing A penalty mechanism is integrated to discourage values from clustering excessively around the imputed central tendency measure This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov–Smirnov test pvalues between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE 0.99 in classical methods such as Mean, KNN, and MICE.>

Experimental Validation

The study was conducted on the UCI Diabetes dataset, where six variables exhibiting biologically implausible zero values were chosen for imputation The KS test observations indicate that quantum-based imputation methods produce significantly lower KS test p-values for features such as SkinThickness, Insulin, BMI, and DiabetesPedigreeFunction Classical methods exhibit minimal Wasserstein distances (all zeros), suggesting that they do not introduce significant changes compared to the original dataset

Conclusion

The findings highlight that the proposed framework enhances reliability in complex datasets by ensuring reconstructed values align more closely with real-world statistical distributions The method successfully diversifies imputed features, redistributing values that were previously concentrated at the mean to exhibit a spread that aligns with natural variability The framework is designed to be computationally scalable and provides a robust solution for imputation tasks in domains such as healthcare and AI pipelines This forward-thinking design positions the method as a promising candidate for future breakthroughs in quantum-enhanced data imputation The final dataset is generated by averaging the values from the three rotated datasets for each imputed feature This pipeline offers a novel approach to handling missing data by integrating statistical imputation, quantum-enhanced transformations, and gradient-free optimization The authors are grateful to the IBM Quantum Experience platform and their team for developing the Qiskit platform and providing open access to their simulators for running quantum circuits and performing the experiments reported here

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Quantum-Inspired Optimization Process for Data Imputation

The method integrates Principal Component Analysis (PCA) with quantum-assisted rotations to reconstruct missing values while preserving statistical fidelity This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov–Smirnov test pvalues between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE 0.99 in classical methods such as Mean, KNN, and MICE.>

Methodology Steps

The imputation process unfolds as follows<ref:2505.04841.

Improvements for AI systems

How to improve data imputation in high-dimensional datasets by integrating PCA with quantum rotations, which enhance statistical integrity and computational efficiency. This improved system can reconstruct missing values while preserving the dataset’s natural variability, as shown by the enhanced variability in mean-imputed features observation.
Implement a hybrid quantum-classical framework that uses classical PCA followed by quantum state encoding and rotation gates to generate rotated principal components, allowing for a more nuanced and statistically valid approach to data reconstruction. This capability allows the system to capture latent structures in missing data, moving beyond rigid deterministic approaches.
Develop an adaptive penalty mechanism within the optimization process that enforces statistical bounds, ensuring that reconstructed values remain within ±2 standard deviations (SD) of the original data distribution. This prevents extreme outliers and ensures that imputed values are constrained to a statistically valid range, addressing the issue where classical methods fail to introduce realistic variability.
Utilize gradient-free optimization algorithms like Differential Evolution or Simulated Annealing to find optimal rotation angles, which allows the system to select the three best angles with the lowest deviation rather than a single absolute optimum. This robustness ensures stability in imputation and provides flexibility for handling complex missing data patterns, as noted by the comparison of optimization methods.
Create a comparative analysis module that uses metrics like Wasserstein distance and Kolmogorov-Smirnov test pvalues to objectively evaluate the performance of quantum methods against classical techniques like Mean or KNN. This system can provide quantitative evidence that quantum-based imputation methods produce significantly lower KS test p-values for features where classical methods show minimal Wasserstein distances (all zeros).

Abstract

Data imputation is a critical preprocessing step, particularly in clinical datasets where missingness can bias downstream inference. We propose a quantum-inspired imputation framework and evaluate it on the UCI Pima Indians Diabetes dataset, where several physiological variables contain structural zeros that are treated as missing. The approach combines Principal Component Analysis (PCA) with quantum rotation-based reconstruction, where rotation angles are selected via gradient-free optimizers (Simulated Annealing, COBYLA, and Differential Evolution). For robustness, we retain the top three optimizer solutions per method and reconstruct missing values under distribution-aware bounds (e.g., plus or minus 2 standard deviations) and avoid unrealistic collapse toward central tendency. We also benchmark against (i) classical baselines (Mean, KNN, MICE, Decision Tree), (ii) modern matrix/ML imputers (SoftImpute, MissForest, VAE), and (iii) rotation/PCA controls (random orthogonal rotations and bootstrap PCA). Across the evaluated features, quantum-inspired variants achieve substantially improved distributional fidelity under Wasserstein W1 relative to modern baselines (e.g., the best quantum setting reduces average W1 by about 66% vs. SoftImpute, about 84% vs. MissForest, and about 90% vs. VAE; and by about 60% vs. Mean imputation), while remaining competitive with strong classical/control configurations. Dispersion is better preserved under the quantum-inspired methods, with variance/SD ratios closer to the observed data than (SoftImpute, MissForest, and VAE) and typically better than (Mean, KNN, MICE, and Decision Tree) on average. Overall, the results support quantum-inspired, optimization-guided rotations as a statistically grounded and scalable strategy for realistic imputation in healthcare and general AI pipelines, with a design that can be mapped to future quantum hardware as it matures.