🤖 AI Summary
This work addresses combinatorial optimization problems—exemplified by Max-Cut—by proposing a class of *sub-universal classical probabilistic variational circuits* based on two-bit random matrices, serving as a strong classical benchmark for quantum variational algorithms such as QAOA. The method replaces quantum circuits with efficient classical probabilistic circuits, enabling scalable parameterization and gradient-based variational optimization; it establishes the first systematic sub-universal classical variational framework. Numerical experiments across diverse graph topologies demonstrate that this classical approach consistently achieves higher Max-Cut solution quality and greater robustness than same-depth QAOA. The study provides a computationally efficient, directly comparable classical reference for assessing quantum advantage, while clarifying the practical applicability limits of quantum variational algorithms in combinatorial optimization and identifying concrete avenues for their improvement.
📝 Abstract
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with sub-universal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.