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Bridging Quantum Computing and Differential Privacy: Insights into Quantum Computing Privacy

Yusheng Zhao, Hui Zhong, Xinyue Zhang, Yuqing Li, Chi Zhang, Miao Pan

TL;DR

The paper addresses privacy in quantum computing by examining quantum differential privacy (QDP) as a principled framework. It develops a taxonomy of QDP implementations across state preparation, quantum circuits, and measurements, emphasizing internal and external randomization and the leveraging of quantum noise in NISQ devices. Key contributions include formal definitions of QDP, bounds based on noise models (e.g., depolarizing channels), and surveys of DP-preserving techniques in state preparation, circuits, and measurements, along with challenges and future directions such as unified benchmarks and privacy auditing. The findings highlight that QDP can be achieved through both natural quantum noise and deliberate perturbations, offering a path toward privacy-preserving quantum algorithms with potential practical impact for sensitive data processing on quantum hardware.

Abstract

While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy tool widely used in the classical scenario, has been extended to the quantum domain, i.e., quantum differential privacy (QDP). QDP may become one of the most promising approaches toward privacy-preserving quantum computing since it is not only compatible with classical DP mechanisms but also achieves privacy protection by exploiting unavoidable quantum noise in noisy intermediate-scale quantum (NISQ) devices. This paper provides an overview of the various implementations of QDP and their performance in terms of privacy parameters under the DP setting. Specifically, we propose a taxonomy of QDP techniques, categorizing the literature on whether internal or external randomization is used as a source to achieve QDP and how these implementations are applied to each phase of the quantum algorithm. We also discuss challenges and future directions for QDP. By summarizing recent advancements, we hope to provide a comprehensive, up-to-date review for researchers venturing into this field.

Bridging Quantum Computing and Differential Privacy: Insights into Quantum Computing Privacy

TL;DR

The paper addresses privacy in quantum computing by examining quantum differential privacy (QDP) as a principled framework. It develops a taxonomy of QDP implementations across state preparation, quantum circuits, and measurements, emphasizing internal and external randomization and the leveraging of quantum noise in NISQ devices. Key contributions include formal definitions of QDP, bounds based on noise models (e.g., depolarizing channels), and surveys of DP-preserving techniques in state preparation, circuits, and measurements, along with challenges and future directions such as unified benchmarks and privacy auditing. The findings highlight that QDP can be achieved through both natural quantum noise and deliberate perturbations, offering a path toward privacy-preserving quantum algorithms with potential practical impact for sensitive data processing on quantum hardware.

Abstract

While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy tool widely used in the classical scenario, has been extended to the quantum domain, i.e., quantum differential privacy (QDP). QDP may become one of the most promising approaches toward privacy-preserving quantum computing since it is not only compatible with classical DP mechanisms but also achieves privacy protection by exploiting unavoidable quantum noise in noisy intermediate-scale quantum (NISQ) devices. This paper provides an overview of the various implementations of QDP and their performance in terms of privacy parameters under the DP setting. Specifically, we propose a taxonomy of QDP techniques, categorizing the literature on whether internal or external randomization is used as a source to achieve QDP and how these implementations are applied to each phase of the quantum algorithm. We also discuss challenges and future directions for QDP. By summarizing recent advancements, we hope to provide a comprehensive, up-to-date review for researchers venturing into this field.
Paper Structure (22 sections, 4 theorems, 35 equations, 2 figures, 4 tables)

This paper contains 22 sections, 4 theorems, 35 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Qubits, quantum gates and circuits
  4. Quantum algorithm
  5. State preparation
  6. Quantum circuit
  7. Quantum measurements
  8. The formulation of classical DP
  9. Differential privacy from classical extension to quantum
  10. The formulation of quantum DP
  11. Quantum noise
  12. A case study: How to obtain QDP using quantum noise?
  13. Differential privacy in noisy quantum algorithms
  14. Differential privacy preservation in state preparation
  15. Differential privacy preservation in a quantum circuit
  16. ...and 7 more sections

Key Result

Theorem 1

If a quantum algorithm $\mathcal{A}=(\phi, \mathcal{E},\{M_i\}_{i\in \mathcal{O}})$ satisfies $(\epsilon,\delta)$-QDP, then for an arbitrary classical mechanism or quantum operation $\mathcal{F}$, $\mathcal{A}_{\mathcal{F}}=\mathcal{F}\circ \mathcal{A}$ also satisfies $(\epsilon,\delta)$-QDP.

Figures (2)

  • Figure 1: Variational quantum algorithm (VQA), taking QML model as an example. The classical part is omitted.
  • Figure 2: (Q)DP of quantum algorithm.

Theorems & Definitions (16)

  • Definition 1: neighboring datasets dwork2014algorithmic
  • Definition 2: global sensitivity dwork2014algorithmic
  • Definition 3: $(\epsilon,\delta)$-DP
  • Definition 4: additive noise mechanism
  • Definition 5: randomized response mechanism
  • Definition 6: $(\epsilon,\delta)$-LDP
  • Definition 7: neighboring quantum states
  • Definition 8: $(\epsilon,\delta)$-QDP
  • Theorem 1: Post-processing dwork2014algorithmiczhou2017differential
  • Theorem 2: Composition hirche2023quantum
  • ...and 6 more