I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. The quantum annealing algorithm is an analogue of simulated annealing, a classical numerical technique which is now obsolete. Hence, I explore strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms, and additionally should be less sensitive to problem mis-specification then the traditional quantum annealing algorithm.
I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. The quantum annealing algorithm is an analogue of simulated annealing, a classical numerical technique which is now obsolete. Hence, I explore strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms, and additionally should be less sensitive to problem mis-specification then the traditional quantum annealing algorithm.
I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm (QAA). Such protocols will have numerous advantages over simple quantum annealing. By using such searches the effect of problem mis-specification can be reduced, as only energy differences between the searched states will be relevant. The QAA is an analogue of simulated annealing, a classical numerical technique which has now been superseded. Hence, I explore two strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms. Specifically, I show how sequential calls to quantum annealers can be used to construct analogues of population annealing and parallel tempering which use quantum searches as subroutines. The techniques given here can be applied not only to optimization, but also to sampling. I examine the feasibility of these protocols on real devices and note that implementing such protocols should require minimal if any change to the current design of the flux qubit-based annealers by D-Wave Systems Inc. I further provide proof-of-principle numerical experiments based on quantum Monte Carlo that demonstrate simple examples of the discussed techniques.
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.
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.
This paper investigates the application of the Quantum Annealing (QA) algorithm to solve complex optimization problems. The core claim is that simulating a complex optimization problem's local search process through the QA's annealing process can effectively locate global optimal solutions. The mechanism involves mapping the solution space of an optimization problem onto the annealing path of QA, controlling the annealing rate and path to guide the solution towards the optimal point. This research leverages QA's inherent ability to mimic physical annealing, aiming to enhance optimization efficiency and accuracy. We present a framework for formulating and applying QA to various complex problems, highlighting its potential advantages over traditional optimization methods. This work contributes to the growing field of quantum computing by demonstrating a practical approach to tackling challenging optimization tasks. The results suggest that QA can be a viable alternative for achieving superior performance in specific optimization scenarios.
This study presents a comprehensive analysis of optimization methodologies in quantum annealing (QA), investigating both theoretical frameworks and practical implementations. We examine various techniques for enhancing quantum annealing performance, including embedding strategies, parameter optimization, and hybrid quantum-classical approaches. Our research identifies critical challenges: qubit connectivity constraints, noise susceptibility, and problem representation difficulties. Through quantitative comparisons of optimization strategies across various problem classes, we establish a systematic framework for evaluating quantum annealing solutions. Results indicate that while significant challenges persist, strategic optimization approaches can substantially improve quantum annealing performance for specific problem domains, suggesting potential quantum advantage for certain complex optimization tasks.
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.