Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Test Case Minimization with Quantum Annealers

Xinyi Wang, Asmar Muqeet, Tao Yue, Shaukat Ali, Paolo Arcaini

TL;DR

BootQA addresses test case minimization (TCM) using quantum annealing by formulating TCM as a QUBO and applying bootstrap sampling to fit hardware limits. The approach yields a generic QUBO formulation and a subproblem decomposition strategy that enables solving large TCM instances on current QA hardware. Empirical results across three real-world datasets show BootQA achieves effectiveness comparable to simulated annealing while offering superior time efficiency relative to other QPU-based methods. The work demonstrates a viable path to practical QA-assisted software testing optimization and provides a public repository for replication.

Abstract

Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum annealers can outperform classical computers. However, the currently available quantum annealers are small-scale, i.e., they have limited quantum bits (qubits); hence, they currently cannot demonstrate the quantum advantage. Nonetheless, research is warranted to develop novel mechanisms to formulate combinatorial optimization problems for quantum annealing (QA). However, solving combinatorial problems with QA in software engineering remains unexplored. Toward this end, we propose BootQA, the very first effort at solving the test case minimization (TCM) problem with QA. In BootQA, we provide a novel formulation of TCM for QA, followed by devising a mechanism to incorporate bootstrap sampling to QA to optimize the use of qubits. We also implemented our TCM formulation in three other optimization processes: classical simulated annealing (SA), QA without problem decomposition, and QA with an existing D-Wave problem decomposition strategy, and conducted an empirical evaluation with three real-world TCM datasets. Results show that BootQA outperforms QA without problem decomposition and QA with the existing decomposition strategy in terms of effectiveness. Moreover, BootQA's effectiveness is similar to SA. Finally, BootQA has higher efficiency in terms of time when solving large TCM problems than the other three optimization processes.

Test Case Minimization with Quantum Annealers

TL;DR

BootQA addresses test case minimization (TCM) using quantum annealing by formulating TCM as a QUBO and applying bootstrap sampling to fit hardware limits. The approach yields a generic QUBO formulation and a subproblem decomposition strategy that enables solving large TCM instances on current QA hardware. Empirical results across three real-world datasets show BootQA achieves effectiveness comparable to simulated annealing while offering superior time efficiency relative to other QPU-based methods. The work demonstrates a viable path to practical QA-assisted software testing optimization and provides a public repository for replication.

Abstract

Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum annealers can outperform classical computers. However, the currently available quantum annealers are small-scale, i.e., they have limited quantum bits (qubits); hence, they currently cannot demonstrate the quantum advantage. Nonetheless, research is warranted to develop novel mechanisms to formulate combinatorial optimization problems for quantum annealing (QA). However, solving combinatorial problems with QA in software engineering remains unexplored. Toward this end, we propose BootQA, the very first effort at solving the test case minimization (TCM) problem with QA. In BootQA, we provide a novel formulation of TCM for QA, followed by devising a mechanism to incorporate bootstrap sampling to QA to optimize the use of qubits. We also implemented our TCM formulation in three other optimization processes: classical simulated annealing (SA), QA without problem decomposition, and QA with an existing D-Wave problem decomposition strategy, and conducted an empirical evaluation with three real-world TCM datasets. Results show that BootQA outperforms QA without problem decomposition and QA with the existing decomposition strategy in terms of effectiveness. Moreover, BootQA's effectiveness is similar to SA. Finally, BootQA has higher efficiency in terms of time when solving large TCM problems than the other three optimization processes.
Paper Structure (23 sections, 14 equations, 3 figures, 4 tables)

This paper contains 23 sections, 14 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Related Work
  4. Quantum annealing for test case minimization
  5. Overview of BootQA
  6. QUBO Formulation for Test Case Minimization
  7. Experiment Design
  8. Research Questions
  9. Experimental Setup and Execution
  10. Evaluation Metrics and Statistical Tests
  11. Evaluation Metrics
  12. Statistical Tests
  13. Experiment Results
  14. RQ1: Effectiveness of QUBO formulation
  15. RQ2: Effectiveness of BootQA compared to VQ
  16. ...and 8 more sections

Figures (3)

  • Figure 1: QUBO formalization for a three-variable problem
  • Figure 2: Overview of BootQA
  • Figure 3: RQ3 -- Objective function ($\mathcal{O}_{\mathit{all}}$) values produced by BootQA and EIDQ for each sub-problem

Theorems & Definitions (5)

  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5