Scalable Quantum Optimisation using HADOF: Hamiltonian Auto-Decomposition Optimisation Framework

Quantum Annealing (QA) and QAOA are promising quantum optimisation algorithms used for finding approximate solutions to combinatorial problems on near-term NISQ systems. Many NP-hard problems can be reformulated as Quadratic Unconstrained Binary Optimisation (QUBO), which maps naturally onto quantum Hamiltonians. However, the limited qubit counts of current NISQ devices restrict practical deployment of such algorithms. In this study, we present the Hamiltonian Auto-Decomposition Optimisation Framework (HADOF), which leverages an iterative strategy to automatically divide the Quadratic Unconstrained Binary Optimisation (QUBO) Hamiltonian into sub-Hamiltonians which can be optimised separately using Hamiltonian based optimisers such as QAOA, QA or Simulated Annealing (SA) and aggregated into a global solution. We compare HADOF with Simulated Annealing (SA) and the CPLEX exact solver, showing scalability to problem sizes far exceeding available qubits while maintaining competitive accuracy and runtime. Furthermore, we realise HADOF for a toy problem on an IBM quantum computer, showing promise for practical applications of quantum optimisation.