Differential Privacy of Quantum and Quantum-Inspired-Classical Recommendation Algorithms
This work addresses privacy concerns in recommendation systems for users and developers, offering a novel analysis that is incremental in applying DP to quantum algorithms.
The paper analyzes the differential privacy (DP) properties of quantum and quantum-inspired-classical recommendation algorithms, finding that the quantum algorithm inherently provides privacy without external noise and both algorithms achieve specific DP bounds, with the quantum version showing better privacy potential.
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 $\big(\tilde{\mathcal{O}}\big(\frac 1n\big),\,\, \tilde{\mathcal{O}}\big(\frac{1}{\min\{m,n\}}\big)\big)$-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.