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.
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.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
This study aims to evaluate the capabilities of state-of-the-art quantum computing applications, with a particular emphasis on their effectiveness in solving optimization problems. Specifically, it focuses on Quantum Annealing algorithms, examining their potential advantages and inherent limitations, reviews the capabilities of existing models, replicates proposed solutions for addressing NP-Hard problems, and systematically compares the results obtained with those produced by classical algorithms. Through this analysis, the study seeks to provide a rigorous assessment of the practical effectiveness of quantum annealing in optimization tasks and its viability as an alternative to classical computational methods in the near future.
Quantum annealing (QA) algorithm is a new quantum optimization algorithm based on the classical simulated annealing (SA) algorithm. Unlike classical SA algorithm, which uses the thermal waves to search for the optimal solution, the QA algorithm uses the quantum tunneling effect to allow a quantum to penetrate a potential barrier with a higher energy than itself. Therefore, the algorithm can get rid of the local extreme values and is more likely to approach the global optimal with higher probability. In the literature, the QA algorithm has shown perfect optimization effects on combinatorial optimization problems. In this paper, the basic concepts and application fields of QA algorithm, which is the core principle of D-Wave quantum computer, are systematically reviewed. The applications of QA algorithm in cryptography, traveling salesman problem, graph coloring problem, and traffic path are discussed in detail. In addition, the direction of future research for QA algorithm is explored.
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'ℏ' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models—double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schrödinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau–Zener tunnelling phenomena is discussed and emphasized.
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.
The Max-Cover is a NP-hard problem. Therefore, the heuristic approach is suitable to solve this problem for large instances. Quantum annealing is a heuristic quantum optimization algorithm that can be used to handle the Max-Cover problem. Recent developments in quantum technology allows creating programmable quantum processors to implement the quantum annealing technique. In this article, we apply the quantum annealing approach to solve the Max-Cover problem. The experimental results show that this approach gives better results than Simulated Annealing in terms of both solution quality and annealing time.