# Quantum Differentially Private Sparse Regression Learning

arXiv: https://arxiv.org/abs/2007.11921 · HTML: https://mlsanity.com/paper/2007.11921/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2020.

## Built on by (most cited first, 18 of 18)

- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [Federated Quantum Machine Learning with Differential Privacy](https://mlsanity.com/paper/2310.06973/) (2023)
- [Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints](https://mlsanity.com/paper/2110.13086/) (2021)
- [Private learning implies quantum stability](https://mlsanity.com/paper/2102.07171/) (2021)
- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)
- [Quantum Machine Learning for Finance](https://mlsanity.com/paper/2109.04298/) (2021)
- [A unifying framework for differentially private quantum algorithms](https://mlsanity.com/paper/2307.04733/) (2023)
- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing](https://mlsanity.com/paper/2406.18651/) (2024)
- [Transition Role of Entangled Data in Quantum Machine Learning](https://mlsanity.com/paper/2306.03481/) (2023)
- [Accelerating variational quantum algorithms with multiple quantum processors](https://mlsanity.com/paper/2106.12819/) (2021)
- [Implementation of Trained Factorization Machine Recommendation System on Quantum Annealer](https://mlsanity.com/paper/2210.12953/) (2022)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction](https://mlsanity.com/paper/2209.12454/) (2022)
- [Generalization Bounds for Quantum Learning via R'enyi Divergences](https://mlsanity.com/paper/2505.11025/) (2025)
- [Privacy Implies Stability: Information-Theoretic Generalization Bounds for Quantum Learning](https://mlsanity.com/paper/2602.01177/) (2026)
- [Characterizing Privacy Risks of Quantum Machine Learning with Emergent Quantum-Native Access](https://mlsanity.com/paper/2609.05702/) (2026)

## Abstract (arXiv)

The eligibility of various advanced quantum algorithms will be questioned if they can not guarantee privacy. To fill this knowledge gap, here we devise an efficient quantum differentially private (QDP) Lasso estimator to solve sparse regression tasks. Concretely, given N d-dimensional data points with Nll d, we first prove that the optimal classical and quantum non-private Lasso requires Omega(N+d) and Omega(√N+√d) runtime, respectively. We next prove that the runtime cost of QDP Lasso is textitdimension independent, i.e., O(N5/2), which implies that the QDP Lasso can be faster than both the optimal classical and quantum non-private Lasso. Last, we exhibit that the QDP Lasso attains a near-optimal utility bound tildeO(N-2/3) with privacy guarantees and discuss the chance to realize it on near-term quantum chips with advantages.