Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Privacy-Preserving Quantum Annealing for Quadratic Unconstrained Binary Optimization (QUBO) Problems

Moyang Xie, Yuan Zhang, Sheng Zhong, Qun Li

TL;DR

This work introduces a privacy-preserving QUBO framework and proposes a novel solution method that employs a combination of digit-wise splitting and matrix permutation to obfuscate the QUBO problem's model matrix Q, effectively concealing the matrix elements.

Abstract

Quantum annealers offer a promising approach to solve Quadratic Unconstrained Binary Optimization (QUBO) problems, which have a wide range of applications. However, when a user submits its QUBO problem to a third-party quantum annealer, the problem itself may disclose the user's private information to the quantum annealing service provider. To mitigate this risk, we introduce a privacy-preserving QUBO framework and propose a novel solution method. Our approach employs a combination of digit-wise splitting and matrix permutation to obfuscate the QUBO problem's model matrix $Q$, effectively concealing the matrix elements. In addition, based on the solution to the obfuscated version of the QUBO problem, we can reconstruct the solution to the original problem with high accuracy. Theoretical analysis and empirical tests confirm the efficacy and efficiency of our proposed technique, demonstrating its potential for preserving user privacy in quantum annealing services.

Privacy-Preserving Quantum Annealing for Quadratic Unconstrained Binary Optimization (QUBO) Problems

TL;DR

This work introduces a privacy-preserving QUBO framework and proposes a novel solution method that employs a combination of digit-wise splitting and matrix permutation to obfuscate the QUBO problem's model matrix Q, effectively concealing the matrix elements.

Abstract

Quantum annealers offer a promising approach to solve Quadratic Unconstrained Binary Optimization (QUBO) problems, which have a wide range of applications. However, when a user submits its QUBO problem to a third-party quantum annealer, the problem itself may disclose the user's private information to the quantum annealing service provider. To mitigate this risk, we introduce a privacy-preserving QUBO framework and propose a novel solution method. Our approach employs a combination of digit-wise splitting and matrix permutation to obfuscate the QUBO problem's model matrix , effectively concealing the matrix elements. In addition, based on the solution to the obfuscated version of the QUBO problem, we can reconstruct the solution to the original problem with high accuracy. Theoretical analysis and empirical tests confirm the efficacy and efficiency of our proposed technique, demonstrating its potential for preserving user privacy in quantum annealing services.
Paper Structure (12 sections, 1 theorem, 11 equations, 3 figures, 1 table, 3 algorithms)

This paper contains 12 sections, 1 theorem, 11 equations, 3 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. The Privacy-preserving QUBO Solving Problem
  3. Our approach
  4. Obtaining the Matrices to Be Sent
  5. Reconstruction of the optimal solution
  6. Performance Analysis
  7. Privacy protection
  8. Accuracy
  9. Efficiency
  10. Evaluation on Accuracy
  11. Related Work
  12. Conclusions and Future Work

Key Result

Theorem 4.1

If the absolute values of all digit matrices' elements follow independently uniform distribution over the digit value space, the probability of recovering a correct $Q^*$ is $\frac{1}{\alpha^{k-1}k!n!}$, where $\alpha$ denotes the number of automorphisms of the sign matrix of $Q$ under the row/colum

Figures (3)

  • Figure 1: Error with different matrix orders and total numbers of matrices when sampling 200 times with a base of 2.
  • Figure 2: Accuracy with different total numbers of samples and orders of model matrix when the number of matrices is 5 with a base of 4.
  • Figure 3: Accuracy with different total numbers of samples and bases of numeral/rounding system when the number of matrices is 5 and the order of model matrix is 40.

Theorems & Definitions (2)

  • Theorem 4.1
  • proof