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Clustering by Contour coreset and variational quantum eigensolver

Canaan Yung, Muhammad Usman

TL;DR

Extensive simulations with synthetic and real‐life data demonstrated that the VQE+Contour Coreset approach outperforms existing QAOA+Coreset k‐means clustering approaches with higher accuracy and lower standard deviation.

Abstract

Recent work has proposed solving the k-means clustering problem on quantum computers via the Quantum Approximate Optimization Algorithm (QAOA) and coreset techniques. Although the current method demonstrates the possibility of quantum k-means clustering, it does not ensure high accuracy and consistency across a wide range of datasets. The existing coreset techniques are designed for classical algorithms and there has been no quantum-tailored coreset technique which is designed to boost the accuracy of quantum algorithms. In this work, we propose solving the k-means clustering problem with the variational quantum eigensolver (VQE) and a customised coreset method, the Contour coreset, which has been formulated with specific focus on quantum algorithms. Extensive simulations with synthetic and real-life data demonstrated that our VQE+Contour Coreset approach outperforms existing QAOA+Coreset k-means clustering approaches with higher accuracy and lower standard deviation. Our work has shown that quantum tailored coreset techniques has the potential to significantly boost the performance of quantum algorithms when compared to using generic off-the-shelf coreset techniques.

Clustering by Contour coreset and variational quantum eigensolver

TL;DR

Extensive simulations with synthetic and real‐life data demonstrated that the VQE+Contour Coreset approach outperforms existing QAOA+Coreset k‐means clustering approaches with higher accuracy and lower standard deviation.

Abstract

Recent work has proposed solving the k-means clustering problem on quantum computers via the Quantum Approximate Optimization Algorithm (QAOA) and coreset techniques. Although the current method demonstrates the possibility of quantum k-means clustering, it does not ensure high accuracy and consistency across a wide range of datasets. The existing coreset techniques are designed for classical algorithms and there has been no quantum-tailored coreset technique which is designed to boost the accuracy of quantum algorithms. In this work, we propose solving the k-means clustering problem with the variational quantum eigensolver (VQE) and a customised coreset method, the Contour coreset, which has been formulated with specific focus on quantum algorithms. Extensive simulations with synthetic and real-life data demonstrated that our VQE+Contour Coreset approach outperforms existing QAOA+Coreset k-means clustering approaches with higher accuracy and lower standard deviation. Our work has shown that quantum tailored coreset techniques has the potential to significantly boost the performance of quantum algorithms when compared to using generic off-the-shelf coreset techniques.
Paper Structure (22 sections, 23 equations, 13 figures, 4 tables, 2 algorithms)

This paper contains 22 sections, 23 equations, 13 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Simulation setup
  3. Proposed framework
  4. Datasets
  5. Quantum circuit parameters optimization and coresets comparing
  6. Analysis method
  7. Contour Coreset -- A new technique for quantum method
  8. Incompatibility of existing coreset to the quantum approach
  9. Contour coreset
  10. Comparison with other coresets
  11. Results and Discussions
  12. Comparison of Coreset Techniques with VQE Algorithm
  13. Optimal VQE setting
  14. Performance under noisy environment
  15. Discussion and outlook
  16. ...and 7 more sections

Figures (13)

  • Figure 1: Framework flowchart. The green and blue areas represent steps done on classical and quantum computers, respectively.
  • Figure 2: VQE circuit. This circuit consists of 5 qubits with 2 repetition of rotation and entanglement blocks.
  • Figure 3: QAOA circuit. This circuit consists of 5 qubits with 5 repetition of rotation and entanglement blocks.
  • Figure 4: Graphical illustration of isotropic Gaussian blobs with uneven distribution. The blue and green dots represent data from two clusters. Subfigure (a), (b) and (c) show the datasets with data ratios 1:2, 4:5 and 1:10 between the two clusters respectively.
  • Figure 5: Graphical illustration of imbalance Lightweight coreset sampling. The dataset consists of two clusters: blue and green dots, with an imbalanced data ratio of 1:10. The five Lightweight coreset points are plotted as red stars. These five coreset points are all clustered within the green majority group, and none are assigned to the blue minority cluster.
  • ...and 8 more figures

Theorems & Definitions (1)

  • Definition A.1: ($\epsilon,k$)-coreset