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 R\'enyi differential privacy (QRDP), which incorporates the advantages of classical R\'enyi DP and is applicable in the QDC domain. Based on the new quantum R\'enyi divergence, QRDP provides delicate and flexible privacy protection by introducing parameter $\alpha$. 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.

翻译：现有量子计算机在噪声中等规模量子（NISQ）状态下仅能操作数百个量子比特，而量子分布式计算（QDC）被视为突破此限制的可靠途径，可使量子计算机充分发挥其计算潜力。然而，与经典分布式计算类似，QDC同样面临隐私泄露问题。现有研究已针对中心化量子计算提出了量子差分隐私（QDP）进行隐私保护，但尚未有专门针对QDC的隐私保护机制。为填补这一研究空白，本文提出了一种称为量子Rényi差分隐私（QRDP）的新概念，该概念融合了经典Rényi差分隐私的优势并适用于QDC领域。基于新型量子Rényi散度，QRDP通过引入参数$\alpha$提供精细且灵活的隐私保护。特别地，QRDP的组合特性非常适合QDC场景，因其能在需要多次量子操作的情况下更精确地控制总体隐私预算。我们分析了多种可实现QRDP的噪声机制，并推导出这些机制所能提供的最低隐私预算。最后，我们研究了不同量子参数对QRDP的影响。通过仿真实验还发现，添加噪声会降低数据可用性，但同时能提升隐私保护水平。