We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to demonstrate the quantum advantage in the search for the ground state(s) through annealing. Quantum annealing as a physical (analog) process to search for the optimal solutions of computationally hard problems are also discussed.
We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to demonstrate the quantum advantage in the search for the ground state(s) through annealing. Quantum annealing as a physical (analog) process to search for the optimal solutions of computationally hard problems are also discussed.
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.
Quantum annealing is a computational paradigm in which optimisation problems are encoded in the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming an initial Hamiltonian into one whose ground state represents the solution, the system navigates complex energy landscapes through a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Quantum annealing is primarily designed for discrete optimisation and sampling tasks and provides a physically motivated heuristic for exploring rugged landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, making them among the largest controllable quantum devices currently available. Beyond optimisation, they also serve as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are challenging to access classically. In this review we introduce the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse the roles of tunnelling, spectral gaps, and open-system effects in determining performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges of benchmarking, scaling, and control. These developments position quantum annealing at the interface of optimisation, stochastic sampling, and programmable quantum dynamics.
This paper explores the potential of integrating quantum annealing principles with quantum algorithms to develop efficient quantum computing solutions. The core concept revolves around a novel algorithm termed "Quantum Annealing Algorithm," which leverages the annealing process to optimize the parameters of quantum algorithms, ultimately enhancing their computational efficiency. This work details the theoretical framework, outlining the mathematical formulation of the algorithm and its key components. We present a methodology for mapping classical optimization problems onto a quantum annealing framework, and discuss strategies for managing the trade-offs between annealing speed and solution quality. The proposed approach offers a potentially transformative method for accelerating quantum computations, particularly for problems exhibiting complex, rugged energy landscapes. The focus remains on the theoretical design and potential benefits, without empirical experimental validation.
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.
Quantum annealing has emerged as a promising approach for solving NP-hard optimization problems, leveraging quantum phenomena such as quantum tunneling to navigate complex energy landscapes. However, the extent to which quantum tunneling contributes to performance enhancements compared to classical methods remains unclear. In this work, we present a comprehensive investigation combining experimental analysis, theoretical modeling, and algorithmic development to characterize when and why quantum annealing provides computational advantages.
We introduce a novel methodology for generating synthetic Quadratic Unconstrained Binary Optimization (QUBO) problems with controlled gradient variance, enabling systematic investigation of landscape characteristics that favor quantum approaches. Our experimental evaluation encompasses four canonical NP-hard problems: Graph Partitioning, Max Cut, Number Partitioning, and Set Cover. Using D-Wave's Advantage2 quantum annealer with 4,400+ qubits, we compare quantum annealing against classical solvers including simulated annealing, stochastic gradient descent, and commercial optimization software.
Our results demonstrate that quantum annealing shows measurable advantages when energy landscapes exhibit high gradient variance (>0.3), suggesting that quantum tunneling effects are most beneficial for rugged optimization landscapes. We provide a theoretical justification for this empirical observation through a WKB-approximation-based model connecting gradient variance to barrier width and tunneling probability. This model achieves R2=0.90 correlation with experimental data and yields quantitative predictions for quantum advantage thresholds.
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.