将大问题拆解为小模块，用量子算法高效求解难解优化问题。
Scalable Quantum Optimisation using HADOF: Hamiltonian Auto-Decomposition Optimisation Framework
- 通过自动分解哈密顿量，分块优化再合并全局解。
- 在超算规模问题上保持高精度，运行时间远优于传统方法。
- 适合想尝试量子优化的科研与工程人员，尤其关注可扩展性。
量子退火（QA）和量子近似优化算法（QAOA）是适用于近期NISQ设备的有前景的优化算法，可用于求解组合优化问题。许多NP难问题可重述为无约束二次二值优化（QUBO），并自然映射到量子哈密顿量。然而，当前NISQ设备的有限量子比特数限制了此类算法的实际部署。本文提出哈密顿量自动分解优化框架（HADOF），采用迭代策略将QUBO哈密顿量自动分解为若干子哈密顿量，分别使用基于哈密顿量的优化器（如QAOA、QA或模拟退火SA）独立优化，并聚合为全局解。实验对比了HADOF与模拟退火（SA）及CPLEX精确求解器，验证其可扩展至远超可用量子比特数的问题规模，同时保持竞争力的准确率与运行时间。此外，我们在IBM量子计算机上实现了该框架在小型示例问题上的应用，展现了量子优化实际应用的潜力。
原文摘要 · Abstract (English)
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.
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