Quantum approximate multi-objective optimization

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.