Differential Privacy Preserving Distributed Quantum Computing

TL;DR

The paper addresses privacy challenges in quantum distributed computing by extending Rényi differential privacy to the quantum domain through QRDP, which uses quantum Rényi divergence and a tunable parameter $\alpha$ to manage privacy budgets in multi-round quantum operations. It defines $(\alpha,\epsilon)$-QRDP, proves post-processing invariance and basic composition, and analyzes several noise mechanisms—Generalized Amplitude Damping, Phase+Amplitude Damping, and Depolarizing channels—for implementing QRDP, deriving corresponding privacy budgets and their impact on data fidelity. The work also connects QRDP to $(\epsilon,\delta)$-QDP, and provides performance evaluations showing the privacy-utility trade-off: increasing noise strengthens privacy (lower $\epsilon$) but reduces utility (lower fidelity), with results largely independent of the specific quantum input state. The findings offer a practical framework for privacy budgeting in QDC, supported by theoretical bounds and simulation-based demonstrations, and point to tunable privacy via inherent noise, QEC, and QEM as meaningful directions for real-world deployment.

Abstract

Existing quantum computers can only operate with hundreds of qubits in the Noisy Intermediate-Scale Quantum (NISQ) state, while quantum distributed computing (QDC) is regarded as a reliable way to address this limitation, allowing quantum computers to achieve their full computational potential. However, similar to classical distributed computing, QDC also faces the problem of privacy leakage. Existing research has introduced quantum differential privacy (QDP) for privacy protection in central quantum computing, but there is no dedicated privacy protection mechanisms for QDC. To fill this research gap, our paper introduces a novel concept called quantum Rényi differential privacy (QRDP), which incorporates the advantages of classical Rényi DP and is applicable in the QDC domain. Based on the new quantum Rényi divergence, QRDP provides delicate and flexible privacy protection by introducing parameter $α$. In particular, the QRDP composition is well suited for QDC, since it allows for more precise control of the total privacy budget in scenarios requiring multiple quantum operations. We analyze a variety of noise mechanisms that can implement QRDP, and derive the lowest privacy budget provided by these mechanisms. Finally, we investigate the impact of different quantum parameters on QRDP. Through our simulations, we also find that adding noise will make the data less usable, but increase the level of privacy protection.

Figures (9)

• Figure 1: Execution of multiple quantum circuit instances with $k$ QPUs.
• Figure 2: Relationship between $\epsilon$ and $\alpha$ under generalized amplitude damping $\gamma$.
• Figure 3: Relationship between $\epsilon$ and $\alpha$ under composition of phase and amplitude damping $\gamma$.
• Figure 4: Relationship between $\epsilon$ and $\alpha$ under composition of phase and amplitude damping $\lambda$.
• Figure 5: Relationship between $\epsilon$ and $\alpha$ under depolarizing mechanism $p$.

Theorems & Definitions (18)

• Definition 1: Classical Differential Privacy
• Definition 2: Quantum Differential Privacy
• Definition 3: Rényi Divergence
• Definition 4: $(\alpha , \epsilon)$-RDP
• Definition 5: Quantum Rényi Divergence
• Definition 6: $(\alpha , \epsilon)$-Quantum Rényi Differential Privacy
• Proposition 1: Post-Processing
• Proposition 2: Basic Composition Theorem
• Proposition 3: Associated Composition Theorem
• Theorem 1: QRDP under Generalized Amplitude Damping