Enhancing combinatorial optimization with classical and quantum generative models

Area of Science:

• Quantum Computing
• Artificial Intelligence
• Financial Optimization

Background:

• Combinatorial optimization algorithms face challenges in efficient search space exploration.
• Generative models offer a novel approach to solving complex optimization problems.

Purpose of the Study:

• Introduce the Generator-Enhanced Optimization (GEO) strategy, a flexible framework for optimization.
• Focus on a quantum-inspired GEO using tensor-network Born machines (TN-GEO).
• Evaluate TN-GEO's performance on the cardinality-constrained portfolio optimization problem.

Main Methods:

• Developed the TN-GEO framework leveraging tensor-network Born machines.
• Constructed portfolio optimization problem instances from S&P 500 and other financial stock indexes.
• Benchmarked TN-GEO against state-of-the-art optimization algorithms.

Main Results:

• TN-GEO demonstrates significant value in an industrial application (portfolio optimization).
• The quantum-inspired generative models exhibit strong generalization capabilities.
• TN-GEO achieves competitive performance, rivaling highly-tuned, decades-old algorithms.

Conclusions:

• TN-GEO represents a powerful new strategy for combinatorial optimization.
• Quantum-inspired models show promise for practical advantage in real-world problems.
• This work paves the way for future applications of quantum generative models.