Sub-universal variational circuits for combinatorial optimization problems
This work addresses combinatorial optimization for researchers in quantum and classical computing, but it is incremental as it builds on existing variational circuit methods.
The paper tackled combinatorial optimization problems by introducing classical probabilistic circuits using two-bit stochastic matrices, and found that these circuits improved performance for several graph types compared to quantum approximate optimization algorithms in solving the Max-Cut problem.
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.