This skill introduces quantum annealing and adiabatic quantum computing as alternative computational models to the gate-based (circuit) approach. Adiabatic quantum computing is an idealised model in which a system changes slowly enough to remain in its lowest-energy state. Quantum annealing is a related metaheuristic that operates in a real, error-prone environment and seeks low-energy solutions without the same guarantee. Learners develop an intuitive understanding of computation expressed as energy minimisation, where solutions correspond to low-energy configurations of a system. The skill differentiates idealised adiabatic quantum computing as a theoretical model from practical quantum annealers inspired by related physical principles, and situates both within the broader landscape of quantum computation.

External: * Basic linear algebra

Internal: * QC1.3 Multi-Qubit Systems and the Gate Model of Quantum Computation

• Distinguish between gate-based quantum computing and annealing or adiabatic computational models at a conceptual level.
• Explain how optimisation problems can be represented as energy minimisation problems and addressed through adiabatic evolution.
• Identify problem classes commonly associated with quantum annealing, including combinatorial optimisation and sampling problems.
• Describe, at a high level, the distinction between ideal adiabatic quantum computing models and practical quantum annealing implementations.
• Explain how practical constraints, such as noise, limited control, restricted connectivity, and embedding overheads, influence the capabilities and interpretation of results from quantum annealers.
• Represent a simple binary optimisation problem using a Quadratic Unconstrained Binary Optimisation (QUBO) or Ising formulation.