This paper describes the logic and creativity needed in order to have high probability of solving discrete optimization problems on a quantum annealing computer.Current features of quantum computing via annealing are discussed.We illustrate the logic at the forefront of this new era of computing, describe some of the work done in this field, and indicate the distinct mindset that is used when programming this type of machine.The traveling salesman problem is formulated for solving on a quantum annealing computer, which illustrates the methods for this computer.
This paper describes the logic and creativity needed in order to have high probability of solving discrete optimization problems on a quantum annealing computer.Current features of quantum computing via annealing are discussed.We illustrate the logic at the forefront of this new era of computing, describe some of the work done in this field, and indicate the distinct mindset that is used when programming this type of machine.The traveling salesman problem is formulated for solving on a quantum annealing computer, which illustrates the methods for this computer.
Most of the modern day computations are considered as an NP-hard like solving a puzzle or traveling salesman problem. Over the decades, engineers are exploring for many approaches of solution, out of which Quantum Annealing has depicted the efficacy. In this paper, we do a review study of Quantum Annealing (i.e., an approach to find the global mini-mum of a particular function that can provide better heuristics for the NP-hard optimization problem) and discussed briefly about quantum computers. Not only that, we also showcase few applications of quantum annealing which include scheduling problem, lung cancer detection, coherence in quantum annealer, and clustering.
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal design of adiabatic algorithms plays an important role in their assessment, we illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP). We demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dynamics are not carefully tailored to the problem. Furthermore we show that inequality constraints, in particular, present a major hurdle for the implementation on analog quantum annealers. We finally argue that programmable digital quantum annealers can overcome many of these obstacles and can - once large enough quantum computers exist - provide an interesting route to using quantum annealing on a large class of problems.
Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional (classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing – highlighting the crucial differences between these two methods – by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems (namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.
Optimization algorithms for combinatorial problems play a critical role in a wide range of applications, from logistics and scheduling to cryptography and artificial intelligence. Traditional classical methods, such as simulated annealing, genetic algorithms, and branch-and-bound techniques, have been widely employed to solve these problems, but they often face limitations in terms of computational efficiency and scalability as problem complexity grows. In recent years, quantum computing has emerged as a promising alternative, with quantum annealing offering a novel approach to solving combinatorial optimization problems. This study provides a comparative analysis of quantum annealing and classical optimization methods, highlighting their respective strengths and limitations. We explore how quantum annealing, through leveraging quantum tunnelling and superposition, has the potential to outperform classical algorithms in specific problem domains and Noisy Mean Field Annealing (NMFA) is used to comparisons of all algorithms. Benchmarking various combinatorial problems, such as the Traveling Salesman Problem (TSP), Max-Cut, Knapsack, and Quadratic Assignment Problem (QAP), this paper discusses performance metrics, computational time, and scalability. The findings suggest that while classical methods remain robust and practical for many real-world problems, quantum annealing holds significant promise, especially as quantum hardware continues to mature. However, there remain challenges in terms of noise, coherence, and problem mapping, which currently limit the full realization of quantum annealing's potential. This study offers insights into the future directions of optimization techniques and the evolving role of quantum computing in solving complex combinatorial problems.
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the Operations Research (OR) and quantum computing communities by helping OR scientists to build initial intuition for-, and offering them a hands-on gateway to quantum-powered methods in the context of discrete optimization. To this end, we consider three quantum-powered optimization approaches that make use of different types of quantum hardware available on the market. To illustrate these approaches, we solve three classical optimization problems: the Traveling Salesperson Problem, Weighted Maximum Cut, and Maximum Independent Set. With a general OR audience in mind, we attempt to provide an intuition behind each approach along with key references, describe the corresponding high-level workflow, and highlight crucial practical considerations. In particular, we emphasize the importance of problem formulations and device-specific configurations, and their impact on the amount of resources required for computation (where we focus on the number of qubits). These points are illustrated with a series of experiments on three types of quantum computers: a neutral atom machine from QuEra , a quantum annealer from D-Wave , and gate-based devices from IBM .
Abstract Traffic optimization remains a significant challenge in urban planning and transportation management. While efficient traffic optimization is crucial for enhancing urban mobility, reducing congestion, and promoting environmental sustainability, traditional computational methods often struggle with the complex, dynamic nature of traffic systems. Recent advances in quantum computing, particularly quantum annealing, offer promising new techniques that could revolutionize traffic flow optimization. This work systematically reviews the literature, starting with search term formulation and ending with the final set of articles. These articles are categorized into three groups: (1) traffic signal control, (2) traffic flow optimization, and (3) routing problems optimization (including vehicle routing problem and traveling salesman problem). The review critically examines current studies on quantum annealing-based traffic optimization, focusing on contributions, methods, solvers, problem suitability, key findings, benchmark fairness, and limitations. It identifies key challenges and provides recommendations for future research. Insights from this work offer researchers and practitioners a concise overview of current challenges and future directions in traffic optimization.