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Harnessing Inherent Noises for Privacy Preservation in Quantum Machine Learning

Keyi Ju, Xiaoqi Qin, Hui Zhong, Xinyue Zhang, Miao Pan, Baoling Liu

TL;DR

This paper mathematically analyzes that the gradient of quantum circuit parameters in QML satisfies a Gaussian distribution, and derive the upper and lower bounds on its variance, which can potentially provide the DP guarantee.

Abstract

Quantum computing revolutionizes the way of solving complex problems and handling vast datasets, which shows great potential to accelerate the machine learning process. However, data leakage in quantum machine learning (QML) may present privacy risks. Although differential privacy (DP), which protects privacy through the injection of artificial noise, is a well-established approach, its application in the QML domain remains under-explored. In this paper, we propose to harness inherent quantum noises to protect data privacy in QML. Especially, considering the Noisy Intermediate-Scale Quantum (NISQ) devices, we leverage the unavoidable shot noise and incoherent noise in quantum computing to preserve the privacy of QML models for binary classification. We mathematically analyze that the gradient of quantum circuit parameters in QML satisfies a Gaussian distribution, and derive the upper and lower bounds on its variance, which can potentially provide the DP guarantee. Through simulations, we show that a target privacy protection level can be achieved by running the quantum circuit a different number of times.

Harnessing Inherent Noises for Privacy Preservation in Quantum Machine Learning

TL;DR

This paper mathematically analyzes that the gradient of quantum circuit parameters in QML satisfies a Gaussian distribution, and derive the upper and lower bounds on its variance, which can potentially provide the DP guarantee.

Abstract

Quantum computing revolutionizes the way of solving complex problems and handling vast datasets, which shows great potential to accelerate the machine learning process. However, data leakage in quantum machine learning (QML) may present privacy risks. Although differential privacy (DP), which protects privacy through the injection of artificial noise, is a well-established approach, its application in the QML domain remains under-explored. In this paper, we propose to harness inherent quantum noises to protect data privacy in QML. Especially, considering the Noisy Intermediate-Scale Quantum (NISQ) devices, we leverage the unavoidable shot noise and incoherent noise in quantum computing to preserve the privacy of QML models for binary classification. We mathematically analyze that the gradient of quantum circuit parameters in QML satisfies a Gaussian distribution, and derive the upper and lower bounds on its variance, which can potentially provide the DP guarantee. Through simulations, we show that a target privacy protection level can be achieved by running the quantum circuit a different number of times.
Paper Structure (13 sections, 2 theorems, 18 equations, 4 figures)

This paper contains 13 sections, 2 theorems, 18 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Differential Privacy and DP-SGD Algorithm
  3. Differential Privacy
  4. DP-SGD Algorithm
  5. NOISY GRADIENTS OF QUANTUM CIRCUIT PARAMETERS
  6. The Impact of Shot Noise and Incoherent Noise on the Output in Quantum Circuits
  7. Analyzing the Variance of the Gaussian Distributed Output with Probabilistic Error Cancellation
  8. Quantum Inherent Noise Mechanism
  9. EVALUATION
  10. Impact of Incoherent Noise on QML
  11. Variance of the Gaussian Distribution Gradient
  12. Privacy Preserving QML
  13. CONCLUTION AND FUTURE WORK

Key Result

Lemma 1

The gradient of the loss function in QML model satisfies a Gaussian distribution with the variance $\text{Var}[\nabla_\theta \ell]$ that is bounded by: where $h_\text{min}=\min\limits_\rho h(p_t,\rho,n)$ and $h_\text{max}=\max\limits_\rho h(p_t,\rho,n)$.

Figures (4)

  • Figure 1: Quantum circuit for 2D classification of Iris dataset.
  • Figure 2: Comparison of test accuracy with and without the use of PEC.
  • Figure 3: (a) The impact of shots on the standard deviation's lower bound. (b) The impact of global depolarizing noise probability on the standard deviation's lower bound.
  • Figure 4: (a) The value of $\epsilon$ in different shots and iterations. (b) The value of $\epsilon$ in different global depolarizing error rates and iterations.

Theorems & Definitions (6)

  • Definition 1: Differential Privacy
  • Definition 2: $l_p$-sensitive
  • Lemma 1
  • proof
  • Theorem 1
  • proof