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Area of Science:

  • Quantum Computing
  • Optimization Algorithms
  • Computational Science

Background:

  • Multi-objective optimization aims to find Pareto fronts, representing optimal trade-offs between competing objectives.
  • Classical methods face challenges in solving multi-objective optimization problems, even when single-objective counterparts are efficient.
  • Quantum computing offers a promising avenue for tackling these complex optimization challenges.

Purpose of the Study:

  • To apply a low-depth quantum approximate optimization algorithm (QAA) to approximate Pareto fronts.
  • To investigate the performance of quantum algorithms on multi-objective weighted maximum-cut problems.
  • To assess the potential of quantum approaches to surpass classical methods in multi-objective optimization.

Main Methods:

  • Implementation of a low-depth quantum approximate optimization algorithm.
  • Demonstration on an IBM Quantum computer.
  • Validation using matrix product state (MPS) numerical simulations.

Main Results:

  • Successful approximation of the optimal Pareto front for multi-objective weighted maximum-cut problems.
  • Empirical performance evaluation on quantum hardware and through simulation.
  • Evidence suggesting potential advantages over classical optimization techniques.

Conclusions:

  • Quantum approximate optimization algorithms are viable tools for multi-objective optimization.
  • Quantum computing demonstrates potential to provide superior solutions for complex trade-off problems.
  • Further research is warranted to explore the full capabilities of quantum algorithms in optimization.