Hybrid Quantum-Classical Framework based on subQUBO and pVSQA

Applying gate-based quantum computers to large-scale constrained combinatorial optimization problems is a significant challenge due to the scalability limits of current quantum hardware. To address these critical challenges, this research proposes a new hybrid quantum-classical framework. The proposed method first employs a classical decomposition technique, called subQUBO, to analyze the full problem space and extract a core subproblem. This decomposition renders large-scale problems to a processable size for current and near-term quantum processors. Next, this subproblem is solved using the postprocessing variationally scheduled quantum algorithm (pVSQA), a quantum variational algorithm with a post-processing step to satisfy problem-specific constraints. The classical decomposition addresses scalability, while pVSQA provides a high-quality, constraint-satisfying solution for the original problem. This method was implemented on the Fujitsu Quantum Simulator, successfully solving a 150-qubit graph min-cut problem, a scale difficult to solve for current gate-based approaches. The results of this research show a pragmatic and promising pathway for leveraging early FTQC-era gate-based quantum computers to tackle complex, real-world optimization problems.