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Quing International Journal of Innovative Research in Science and Engineering

A Comprehensive Review of Quantum Annealing for Combinatorial Routing Problems

A. Karunamurthy, V. Vasanth

Published Dec 30, 2023• 0 citations
Publisher
DOI
10.54368/qijirse.2.4.0011

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Combinatorial optimization is a foundation of numerous scientific, industrial, and social decision-making questions, but its usefulness is mostly restricted by the exponential complexity of the problem of classical computability. The quantum annealing (QA) has become one of the leading analogue quantum systems to address such problems, whereby optimization problems are converted into physical energy structures and quantum fluctuations are utilized to perform systematic exploration. It provides a critical, synthesized, and comprehensive review of quantum annealing as applied to combinatorial optimization, including the theoretical basis, hardware designs, algorithm methods, issues of embedding and encoding, benchmarking procedures, applications, and integration with quantum algorithms based on gates and solvers on a classical computer. We build a comprehensive taxonomy between adiabatic dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to state-of-the-art flux-qubit annealers, new architectures, and hybrid quantum classical pipelines. We show that the overhead of embedding and encoding and the benchmarking approach taken are the most significant factors in determining scalability and performance, but not the raw number of qubits. Transportation, energy systems, robotics, finance, pharmacological discovery, and machine learning are just some examples of the domain-specific case studies that use QA with minimal empirical utility as a hybrid refinement engine and not an independent solver. Moreover, we introduce a stringent evaluation of the existing benchmarking culture, clarify the causal links between QA and QAOA as well as between VQE and structural predicaments, and reveal the institutional roots of the existing restrictions. We conclude by identifying a research roadmap in the future, focusing on the annealing hardness characterization, Stoquastic control manipulation, embedding rules automation, architecture design, and development of principled quantum advantage. It creates a benchmark reference to those in the field and research and deployment of scalable, reliable, and application-relevant quantum optimization

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Combinatorial optimization is a foundation of numerous scientific, industrial, and social decision-making questions, but its usefulness is mostly restricted by the exponential complexity of the problem of classical computability. The quantum annealing (QA) has become one of the leading analogue quantum systems to address such problems, whereby optimization problems are converted into physical energy structures and quantum fluctuations are utilized to perform systematic exploration. It provides a critical, synthesized, and comprehensive review of quantum annealing as applied to combinatorial optimization, including the theoretical basis, hardware designs, algorithm methods, issues of embedding and encoding, benchmarking procedures, applications, and integration with quantum algorithms based on gates and solvers on a classical computer. We build a comprehensive taxonomy between adiabatic dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to state-of-the-art flux-qubit annealers, new architectures, and hybrid quantum classical pipelines. We show that the overhead of embedding and encoding and the benchmarking approach taken are the most significant factors in determining scalability and performance, but not the raw number of qubits. Transportation, energy systems, robotics, finance, pharmacological discovery, and machine learning are just some examples of the domain-specific case studies that use QA with minimal empirical utility as a hybrid refinement engine and not an independent solver. Moreover, we introduce a stringent evaluation of the existing benchmarking culture, clarify the causal links between QA and QAOA as well as between VQE and structural predicaments, and reveal the institutional roots of the existing restrictions. We conclude by identifying a research roadmap in the future, focusing on the annealing hardness characterization, Stoquastic control manipulation, embedding rules automation, architecture design, and development of principled quantum advantage. It creates a benchmark reference to those in the field and research and deployment of scalable, reliable, and application-relevant quantum optimization
This paper investigates the application of quantum annealing to address the challenges of combinatorial optimization within large-scale network routing. Traditional classical algorithms frequently encounter significant computational bottlenecks when attempting to determine optimal routes across complex networks, often failing to scale effectively with increasing network size and complexity. Quantum annealing offers a potentially transformative approach by leveraging quantum mechanical effects to explore solution spaces more efficiently. This work outlines a methodology for mapping network routing problems – characterized by a vast number of possible routes – onto the quantum annealing hardware. We present a model for representing the problem, formulating it as an Ising model, and then detail the annealing process. The core claim is that quantum annealing can provide a viable solution for optimizing network routes, particularly in scenarios where classical methods are computationally intractable. We explore the underlying principles of quantum annealing, focusing on its ability to escape local minima and achieve a lower energy state, representing the optimal solution. The research aims to demonstrate the feasibility and potential advantages of employing quantum annealing in practical network routing applications, paving the way for more efficient and robust network designs.
Enhancing the efficiency, safety, and speed of large-scale Automated Guided Vehicle (AGV) systems is critical to increasing the productivity of logistics warehouses. Studies using the latest quantum annealers such as "D-Wave Advantage" with over 5000 qubits have shown the potential of quantum annealing (QA) to rapidly optimize AGV routing. However, applying QA to complex and large-scale AGV routing problems is a challenging task due to insufficient consideration of intricate operational conditions, and also due to the insufficient number of qubits in quantum annealers. This paper proposes a refined combinatorial optimization problem that minimizes the total travel time of thousands of AGVs while enhancing safety and efficiency by avoiding collisions. To solve such large-scale optimization problems with thousands of variables, we also propose a novel system architecture containing a Simulated Quantum Annealing (SQA) accelerator using multiple FPGAs. The proposed SQA accelerator is capable of processing problems with over 50,000 variables, which could be a few tens to several hundred times larger than the problems processed on the "D-Wave Advantage". It addresses multiple combinatorial optimization problems across multiple FPGAs concurrently while processing each problem in a high degree of parallelism. We demonstrate the accurate operation of the proposed SQA accelerator using a real-world large-scale AGV system with over 1000 AGVs. According to the experimental results, we observed faster processing speed and better quality results over existing SQA solvers.