Adaptive Qubit Freezing Enables Robust Graph Partitioning for Divide-and-Conquer QAOA

Abstract

Abstract Separator-based divide-and-conquer QAOA can address graphs wider than the qubit capacity of one circuit, meaning the number of physical qubits usable by that circuit, but the Large Graph Partitioner (LGP) in DC-QAOA aborts when no small vertex separator exists. We introduce Frozen Large Graph Partitioning (FrozenLGP), a three-phase extension of this specific pipeline. It first runs standard LGP (Phase 1); after failure, it freezes a minimum node cut of each selected residual graph, conditional on the first budget-feasible separator (Phase 2); and it uses a deterministic width-feasible split as Coverage-Preserving Partitioning (CPP) for a final fallback (Phase 3). For a fixed frozen spin assignment, removed Ising couplings are folded exactly into local fields; assignment selection, QAOA, truncated reconstruction, and fallback ranking remain approximate. On the pooled high-connectivity partition benchmarks (n ≤ 1000), the scalable driver achieves 89.8% separator-based coverage without the CPP fallback at freeze budget B_f = 3, compared with 4.6% for standard LGP alone. In the 100-instance end-to-end benchmark, FrozenLGP's Phase 2 increases coverage without CPP from 76 to 91 instances in the selected best-restart outcomes. The deterministic CPP fallback handles the remaining nine. CPP-inclusive coverage is 100%, including all tested partitioning instances up to 10^4 vertices. This is a termination guarantee, not a measure of freezing-based recovery. When Phase 1 succeeds, both methods follow identical seeded circuit paths and attain identical approximation ratios. Compared with QAOA-in-QAOA, FrozenLGP achieves higher mean approximation ratios at each measured size, at the cost of more invoked subcircuit solves and greater aggregate quantum work. Under two simulated noise channels, the coverage extension persists while the reported output distributions of every method degrade under the stronger channel. In simulation, these results support FrozenLGP as a topology-robust front end for separator-based divide-and-conquer QAOA.