Differential Privacy of Quantum and Quantum-Inspired-Classical Recommendation Algorithms

2025-02-07

AI Summary

This work systematically investigates the differential privacy (DP) properties of quantum recommendation algorithms and quantum-inspired classical recommendation algorithms. Theoretically, under reasonable assumptions, both classes satisfy (Õ(1/n), Õ(1/min{m,n}))-DP; however, quantum recommendation algorithms inherently possess privacy-preserving clipping—requiring no external noise—and are rigorously proven for the first time to satisfy DP intrinsically. For classical SVD and low-rank approximation, we propose a novel perturbation mechanism that improves the privacy–utility trade-off. Empirical evaluation and theoretical analysis jointly demonstrate that quantum algorithms provide stronger privacy guarantees than their quantum-inspired classical counterparts at equivalent accuracy, revealing significantly greater inherent privacy potential. This work establishes a foundational theoretical framework for privacy in quantum machine learning.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Bias, Fairness & Privacy
• Philosophy and Ethics of AI: Privacy & Security

Application Category

• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are $ig( ilde{mathcal{O}}ig(frac 1nig),,, ilde{mathcal{O}}ig(frac{1}{min{m,n}}ig)ig)$-DP under some reasonable restrictions, where $m$ and $n$ are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

Problem

• Analyzing DP properties of quantum algorithms
• Introducing perturbation method for SVD
• Comparing privacy in quantum vs classical algorithms

Innovation

• Quantum algorithm ensures intrinsic privacy
• Novel SVD perturbation method introduced
• Quantum outperforms classical in privacy