Quantum Optimization Algorithms.

Tad Hogg, Dmitriy Portnov

Jincheng Zhang

Quantum Optimization Algorithms (QOA) represent a paradigm shift in optimization techniques, leveraging the unique properties of quantum mechanics to potentially achieve exponential speedups compared to classical algorithms. This paper introduces a novel QOA framework based on the manipulation of quantum entanglement to facilitate efficient and robust optimization. We outline the core mechanism, detailing the algorithmic steps and their mathematical foundations. The research explores the potential of QOA to address limitations in traditional optimization methods, particularly concerning the complexity of certain optimization problems. This work serves as a foundation for further investigation and development into practical quantum optimization solutions.

Tomohiro Hattori, Takuya Hatomura

Feedback-based quantum optimization is a quantum approach to combinatorial optimization. In this paper, we introduce the classical counterpart of feedback-based quantum optimization by using the quantum-classical correspondence of spin systems to discuss the possibility of quantum advantage. It also enables us to develop higher-order theory of a previously proposed classical approach to feedback-based quantum optimization. First, we compare the feedback-based algorithm for quantum optimization (FALQON) and its variant with their classical counterparts. Then, we perform benchmark tests of various quantum and classical algorithms with small-scale instances, and of classical algorithms with large-scale instances. Main findings are that (i) quantum algorithms can be advantageous to classical algorithms in terms of the quality of solutions, while classical algorithms tend to show faster convergence than quantum ones, and (ii) one of the classical algorithms discussed in this paper shows significant scalability for higher-order unconstrained binary optimization problems. These findings highlight the importance of quantumness and the usefulness of classical approaches.

Bhagvan Kommadi

This chapter covers an overview of quantum optimization algorithms. You will see how quantum optimization is used in real life. Code examples are presented for the quantum optimization applications.

Ojas Parekh

Jesse Van Griensven Thé, Roydon Andrew Fraser, José R. Rosas-Bustos