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[2502.04758] Differential Privacy of Quantum and Quantum-Inspired Classical Recommendation Algorithms
Summary
The paper explores the differential privacy of quantum and quantum-inspired classical recommendation algorithms, demonstrating their inherent privacy mechanisms without additional noise injection.
Why It Matters
As data privacy becomes increasingly critical, understanding how quantum algorithms can maintain differential privacy offers insights into developing secure recommendation systems. This research bridges quantum computing and classical methods, potentially influencing future AI applications in privacy-sensitive domains.
Key Takeaways
- Quantum recommendation algorithms can achieve differential privacy without extra noise.
- The study introduces a perturbation technique for low-rank matrix reconstruction.
- Findings validate the privacy guarantees using real-world datasets.
- The research highlights the scalability of quantum algorithms in privacy contexts.
- Implications for future AI systems in maintaining user privacy.
Quantum Physics arXiv:2502.04758 (quant-ph) [Submitted on 7 Feb 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:Differential Privacy of Quantum and Quantum-Inspired Classical Recommendation Algorithms Authors:Chenjian Li, Mingsheng Ying, Ji Guan View a PDF of the paper titled Differential Privacy of Quantum and Quantum-Inspired Classical Recommendation Algorithms, by Chenjian Li and 1 other authors View PDF HTML (experimental) Abstract:We study the differential privacy (DP) of the quantum recommendation algorithm of Kerenidis--Prakash and its quantum-inspired classical counterpart. Under standard low-rank and incoherence assumptions on the preference matrix, we show that the randomness already present in the algorithms' measurement/$\ell_2$-sampling steps can act as a privacy-curating mechanism, yielding $(\varepsilon,\delta)$-DP without injecting additional DP noise through the interface. Concretely, for a system with $m$ users and $n$ items and rank parameter $k$, we prove $\varepsilon=\mathcal O(\sqrt{k/n})$ and $\delta= \mathcal O\big(k^2/\min^2\{m,n\}\big)$; in the typical regime $k=\mathrm{polylog}(m,n)$ this simplifies to $\varepsilon=\tilde{\mathcal O}(1/\sqrt n)$ and $\delta=\tilde{\mathcal O}\big(1/\min^2\{m,n\}\big)$. Our analysis introduces a perturbation technique for truncated SVD under a single-entry update, which tracks the induced change in the low-rank reconstruction while avoiding unstable singular-vector comparisons. Finally, we validate t...