Solving Combinatorial Optimization Problems with a Block Encoding Quantum Optimizer

Abstract: In the pursuit of achieving near-term quantum advantage for combinatorial optimization problems, the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) are the primary methods of interest, but their practical effectiveness remains uncertain. Therefore, there is a persistent need to develop and evaluate alternative variational quantum algorithms. This study presents an investigation of the Block ENcoding Quantum Optimizer (BENQO), a hybrid quantum solver that uses block encoding to represent the cost function. BENQO is designed to be universally applicable across discrete optimization problems. Beyond Maximum Cut, we evaluate BENQO's performance in the context of the Traveling Salesperson Problem, which is of greater practical relevance. Our findings confirm that BENQO performs significantly better than QAOA and competes with VQE across a variety of performance metrics. We conclude that BENQO is a promising novel hybrid quantum-classical algorithm that should be further investigated and optimized to realize its full potential.