Optimization Algorithms for Combinatorial Problems: A Comparative Study of Quantum Annealing and Classical Methods

Abstract

Recently, a pair of quantum-annealing-inspired techniques (QAIA) have been presented for effectively resolving multimodal optimization challenges. These methods involve simulated splitting and several variations of the modelled coherently Ising device. Quantum annealing, a quantum computing paradigm, leverages quantum mechanics to explore solution spaces and promises advantages in solving certain classes of optimization problems more efficiently.  Regulated evaluations between these techniques, along with other physics-based methods, are required to verify their supremacy. In this study, we compare QAIA to quantum cooling and other physics-based methods for Max-Cut issues with up to 20,000 nodes. In comparison to classical heating, we discovered that rapid modelled splitting performed exceptionally well for hybrid and tiny business graphs, delivering a time-to-solution decrease of around 50 times. If you want to find the highest cut value in Pegasus graphs, discrete simulated bifurcation works better than the D-Wave Advantage method and takes the least amount of time to reach your goal for large graphs. According to our findings, QAIA is a viable approach to practical combinatorial optimization issues and can serve as a suitable starting point for rival quantum algorithms. Finding the ideal object among a group of possibilities is known as algorithmic optimization, and it is a common problem in many fields of study, including computer science, mathematical applications, and probabilistic physics.