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An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization.

Zeguan Wu1, Mohammadhossein Mohammadisiahroudi1, Brandon Augustino1

  • 1Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA 18015, USA.

Entropy (Basel, Switzerland)
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Summary

This study introduces an inexact-feasible quantum-assisted interior point method (IF-QIPM) to address challenges in quantum computing. The new quantum linear system algorithm (QLSA) offers a dimension speedup for optimization problems like support vector machines.

Keywords:
interior point methodquadratic optimizationquantum computing

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Area of Science:

  • Quantum computing
  • Optimization algorithms
  • Machine learning

Background:

  • Quantum linear system algorithms (QLSAs) promise to accelerate computations involving linear systems.
  • Interior point methods (IPMs) are crucial for solving optimization problems, requiring Newton linear systems at each step.
  • Current quantum-assisted IPMs (QIPMs) face limitations due to quantum computer noise, yielding inexact solutions.

Purpose of the Study:

  • To develop a novel quantum-assisted interior point method (QIPM) that can handle inexact solutions from QLSAs.
  • To address the issue of infeasible solutions typically arising from inexact search directions in QIPMs.
  • To apply the proposed method to support vector machine (SVM) problems and analyze its performance.

Main Methods:

  • Proposed an inexact-feasible QIPM (IF-QIPM) designed to manage inexact solutions from quantum linear system algorithms.
  • Applied the IF-QIPM to solve ℓ1-norm soft margin support vector machine (SVM) problems.
  • Analyzed the computational complexity and demonstrated a speedup in the dimension compared to existing methods.

Main Results:

  • The IF-QIPM successfully handles inexact solutions from QLSAs, overcoming the infeasibility problem.
  • Demonstrated a significant speedup in computational complexity with respect to the dimension for SVM problems.
  • Achieved a complexity bound superior to existing classical and quantum algorithms that yield classical solutions.

Conclusions:

  • The developed IF-QIPM effectively integrates quantum linear system algorithms into interior point methods.
  • This approach offers a promising direction for accelerating optimization problems, particularly in machine learning contexts like SVMs.
  • The algorithm provides a new state-of-the-art complexity bound for solving such problems.