Solving Combinatorial Optimization Problems on a Photonic Quantum Computer

Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration into alternative paradigms such as quantum computing. In this paper, we investigate the application of photonic quantum computing to solve combinatorial optimization problems. Leveraging the principles of quantum mechanics, we demonstrate how photonic quantum computers can efficiently explore solution spaces and identify optimal solutions for a range of combinatorial problems. We provide an overview of quantum algorithms tailored for combinatorial optimization for different quantum architectures (boson sampling, quantum annealing and gate-based quantum computing). Additionally, we discuss the advantages and challenges of implementing those algorithms on photonic quantum hardware. Through experiments run on an 8-qumode photonic quantum device, as well as numerical simulations, we evaluate the performance of photonic quantum computers in solving representative combinatorial optimization problems, such as the Max-Cut problem and the Job Shop Scheduling Problem.