Title: Differential Privacy of Hybrid Quantum-Classical Algorithms
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Quantum differential privacy, hybrid quantum-classical algorithms, noise mechanism

Abstract: Differential privacy has been successfully used to safeguard the privacy of classical algorithms and has more recently been extended to protect the privacy of quantum algorithms. However, in the present era of Noisy Intermediate-Scale Quantum (NISQ) computing, practical applications are
limited to hybrid quantum-classical algorithms (e.g., quantum machine learning and variational quantum algorithms) to tackle computational tasks due to inherent quantum noise. Unfortunately, the issue of privacy in such algorithms has been largely disregarded. This paper addresses this gap by defining the differential privacy of quantum measurements as a means to protect the overall privacy of hybrid quantum-classical algorithms. The core concept involves the use of differentially private quantum measurements to ensure privacy since hybrid quantum-classical algorithms heavily rely on quantum measurements for the interaction between quantum and classical computing. To address this, we explore post-processing and composition theorems to establish the efficiency and feasibility of differentially private quantum measurements. By introducing quantum depolarizing noise or a unique classical noise (measurement-based exponential mechanisms) into quantum measurements, we bolster the security of algorithms against privacy violations. Taking the hybrid nature of differentially private quantum measurements, our framework offers both classical and quantum differential privacy. To validate these theoretical results, we carry out various numerical experiments demonstrating the effectiveness and practicality of our framework using differentially private quantum measurements to protect the privacy of hybrid quantum-classical algorithms.