Differential Privacy for Hybrid Quantum-Classical Algorithms: Frameworks, Mechanisms, and Applications in Quantum Machine Learning
- Publication Type:
- Thesis
- Issue Date:
- 2025
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Differential privacy is a mathematical framework for protecting individual data in algorithmic outputs, ensuring that small changes to the input do not significantly alter the output distribution. It has become a cornerstone of privacy-preserving data analysis and machine learning in classical settings, and has recently been extended to quantum computing to safeguard information encoded in quantum states. However, in the Noisy Intermediate-Scale Quantum (NISQ) era, where practical quantum applications rely heavily on hybrid quantum-classical algorithms due to inherent quantum noise, the integration of differential privacy in such algorithms has been largely overlooked.
This thesis fills that gap by proposing a hybrid quantum-classical differential privacy (HDP) framework tailored for hybrid algorithms with fixed quantum measurements, which serve as the primary interface between quantum and classical systems. We focus on designing differentially private quantum measurements using both quantum depolarizing noise and a measurement-based exponential mechanism (MBEM), which enables privacy guarantees while preserving utility in practical hybrid settings. To ensure robustness under post-processing and composability under repeated measurements, we establish post-processing and composition theorems within the HDP framework. We validate these theoretical results through extensive numerical experiments on various quantum circuits, demonstrating the practical effectiveness of our approach in preserving privacy with manageable utility trade-offs.
Furthermore, we investigate Rényi Differential Privacy (RDP), a refinement of standard differential privacy with strong composability and tunable privacy-utility trade-offs, in the context of quantum machine learning (QML). QML algorithms, typically implemented via hybrid quantum-classical procedures, use fixed quantum measurements to extract classical outputs from quantum states. Leveraging the Heisenberg picture, we formulate RDP in terms of Rényi divergence between measurement-induced output distributions and derive analytically tractable upper bounds for certifying privacy guarantees. Our results demonstrate that QML provides a principled and tractable pathway for privacy analysis, bridging classical RDP techniques with practical quantum learning systems.
Together, these contributions form a unified and practical approach for achieving differential privacy in hybrid quantum-classical algorithms, offering rigorous tools for privacy-preserving quantum machine learning on real-world NISQ systems.
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