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Computer Engineering and Science

Survey of adiabatic quantum optimization algorithms

Yingyi Zhang

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Adiabatic quantum optimization was first proposed in 2001,which was attended to solve the NPC combinatorial optimization problems,and soon became one of the hot topics in quantum computation.This survey reviews the progress in the field of adiabatic quantum optimization in the past decade,and summarizes the key methods and techniques used in the studies of adiabatic quantum optimization algorithms.Finally,this survey is concluded by predicting the future of the field.

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Adiabatic quantum optimization was first proposed in 2001,which was attended to solve the NPC combinatorial optimization problems,and soon became one of the hot topics in quantum computation.This survey reviews the progress in the field of adiabatic quantum optimization in the past decade,and summarizes the key methods and techniques used in the studies of adiabatic quantum optimization algorithms.Finally,this survey is concluded by predicting the future of the field.
The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of these new devices. These problems are recurrent in industrial applications and they are in general difficult for classical computing hardware. In this work, we provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. We focus mainly on four different approaches including digitizing the adiabatic quantum computing, global quantum optimization algorithms, the quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. We also discuss the quantum algorithms that are custom designed to solve certain types of QUBO problems.
This review provides a comprehensive introduction to the current state of optimization through quantum computing, as well as its main methods and highlights. It begins with an overview of the history and principles of quantum computing, followed by a concise explanation of classical optimization techniques. References to key mathematical tools essential for understanding quantum optimization are introduced to assist readers new to the field. The review then explores various quantum optimization techniques, categorized by hardware requirements, pipelining strategies, kernel methods, order, continuity, heuristic and metaheuristic approaches. Graphs and charts are included to illustrate the interconnections between these techniques, enhancing understanding of their complementarity. Finally, the review concludes with some considerations about societal, economic and environmental impacts and a detailed table summarizing the different methods and their applications.
Quantum computing has emerged as a transformative technology, particularly for solving optimization problems, which are notoriously difficult for classical computers. Quantum algorithms, leveraging quantum parallelism and entanglement, promise significant speedups for a wide range of optimization tasks, from combinatorial optimization to machine learning. This paper reviews recent advancements in quantum algorithms for optimization problems, highlighting key algorithms such as Grover’s search algorithm, the Quantum Approximate Optimization Algorithm (QAOA), and the Quantum Alternating Operator Ansatz (QAOA). We also explore the challenges and potential of quantum computing in addressing real-world optimization problems, such as in logistics, finance, and machine learning. The paper discusses the current state of quantum hardware, as well as theoretical and practical limitations in implementing these quantum algorithms. Finally, we propose future research directions to overcome existing challenges and enhance the application of quantum algorithms in solving complex optimization problems
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The quantum meta heuristic algorithm is developed by applying quantum computing to the meta-heuristic algorithm.This kind of algorithm is good at solving combinatorial and numerical optimization problems,and has the characteristics of acce-lerated convergence,enhanced exploration and development capabilities,and can obtain higher performance results than traditional meta-heuristic algorithms.This paper mainly summarizes and reviews the theoretical methods and applications of quantum meta-heuristic algorithms.Firstly,this paper expounds the basic concepts and principles of quantum computing,and analyzes the challenging problems that need to be solved urgently in the field of quantum computing.Then,this paper expounds the basic principles of six classical quantum meta-heuristic algorithms,analyzes the latest research progress,gives their advantages and disadvantages in solving domain-specific problems,and demonstrates the application of quantum meta-heuristic algorithms in different disciplines and engineering scenarios.Finally,this paper analyzes and explores the existing problems in the theories and methods of quantum meta-heuristic algorithms,and summarizes the future development direction of the theory and application of quantum meta-heuristic algorithms.
QUBO problems are NP-hard and have wide applications in optimization, including finance, logistics, machine learning, and combinatorial problems. However, classical algorithms employed for solving them can often get stuck in local minima. This paper presents an Adiabatic Quantum Computing (AQC) approach towards finding an optimal solution for QUBO problems. The QUBO problem has been first encoded into Hamiltonians. The adiabatic theorem has been used to achieve success of an AQC solution with a rate which is found to be dependent on relative gap between the ground state and first exited state of the Hamiltonian.