The application of quantum computing to data management has attracted growing interest, yet remains constrained by a limited understanding of how the physical behaviour of quantum devices relates to the structure and difficulty of database problems. In particular, evaluating quantum annealing approaches for combinatorial optimisation, which is central to many data management tasks, poses significant challenges beyond the scope of conventional empirical and complexity-theoretic methods.
We present a computational toolbox for the systematic numerical analysis of quantum annealing processes derived from data management problem formulations. Adopting a physics-informed perspective, the toolbox enables the study of spectral and dynamical properties -- such as energy gaps and eigenstate structure -- that are inaccessible through direct hardware measurements, yet essential for understanding computational hardness and scaling behaviour.
Our approach further provides derived quantities and visualisation techniques that support the interpretation of optimisation dynamics, the identification of structural similarities to canonical physical models, and the construction of reduced effective descriptions. By bridging methodological gaps between quantum computing and database systems research, this work establishes a principled foundation for evaluating quantum approaches and guiding future co-design efforts.
The application of quantum computing to data management has attracted growing interest, yet remains constrained by a limited understanding of how the physical behaviour of quantum devices relates to the structure and difficulty of database problems. In particular, evaluating quantum annealing approaches for combinatorial optimisation, which is central to many data management tasks, poses significant challenges beyond the scope of conventional empirical and complexity-theoretic methods.
We present a computational toolbox for the systematic numerical analysis of quantum annealing processes derived from data management problem formulations. Adopting a physics-informed perspective, the toolbox enables the study of spectral and dynamical properties -- such as energy gaps and eigenstate structure -- that are inaccessible through direct hardware measurements, yet essential for understanding computational hardness and scaling behaviour.
Our approach further provides derived quantities and visualisation techniques that support the interpretation of optimisation dynamics, the identification of structural similarities to canonical physical models, and the construction of reduced effective descriptions. By bridging methodological gaps between quantum computing and database systems research, this work establishes a principled foundation for evaluating quantum approaches and guiding future co-design efforts.
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.
Quantum annealing has emerged as a transformative approach in solving combinatorial optimization problems by leveraging the principles of quantum mechanics. A comprehensive survey of quantum annealing is presented, delineating its foundational concepts, state-of-the-art advancements, and diverse applications across domains such as logistics, finance, machine learning, and energy optimization. Notable contributions include the introduction of a systematic benchmarking framework to evaluate quantum annealing against classical optimization techniques across metrics like time-to-target, scalability, and energy efficiency. Additionally, novel hybrid quantum-classical paradigms and hardware advancements are explored, addressing challenges in qubit connectivity, coherence, and noise resilience. Optimization problems are mapped to suitable quantum annealing platforms, offering practical guidelines for leveraging quantum technologies in real-world scenarios. Critical gaps in scalability and integration with machine learning are identified, with future research directions proposed to bridge these challenges. These findings provide a holistic understanding of quantum annealing's potential, offering a foundational resource for advancing quantum computing in optimization.
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
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.