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

2025-10-03

AI Summary

Current NISQ devices, constrained by limited qubit counts, struggle to solve large-scale QUBO-formulated NP-hard problems using quantum algorithms such as QAOA and quantum annealing. Method: This paper proposes HADOF—a hybrid adaptive decomposition framework—that introduces a novel Hamiltonian self-decomposition mechanism. It iteratively and automatically decomposes the QUBO Hamiltonian into smaller subproblems solvable on small-scale quantum hardware, enabling collaborative optimization of massive instances. Contribution/Results: HADOF unifies support for hybrid solvers including QAOA, quantum annealing, and simulated annealing. Experimental validation on both classical simulators and real quantum hardware demonstrates its ability to handle problem sizes far exceeding current chip capacities. It achieves solution accuracy comparable to CPLEX while significantly outperforming simulated annealing in scalability—thus striking an effective balance between scalability and high solution fidelity.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• Scaling quantum optimization for large combinatorial problems
• Overcoming limited qubit counts in NISQ quantum devices
• Automatically decomposing QUBO Hamiltonians into solvable subproblems

Innovation

• Automatically decomposes QUBO Hamiltonians into subproblems
• Uses iterative strategy with quantum annealing optimizers
• Enables scalable optimization beyond current qubit limits