How Much Reconstruction Does Quantum Machine Learning Need? Late Fusion of Uncoupled Quantum Subcircuits

원문 초록

Circuit cutting lets a large quantum neural network (QNN) run as independent subcircuits on small devices, but rebuilding its outputs by quasiprobability reconstruction carries a classical sampling overhead exponential in the number of cuts. This paper asks whether machine-learning tasks need this step. We replace it with late fusion: subcircuits are trained without cross-cut coupling, and a small classical head combines their local measurements at a cost constant in the cut count. To characterize the trade-off, we introduce a reconstruction dial $Q$, a physically executable budget that retains a fraction of the quasiprobability terms, and a cut-entanglement diagnostic that indicates, within a fixed scale, how much reconstruction a task needs (Spearman $\rho=0.59$ over $104$ runs). Across synthetic and standard datasets, uncoupled late fusion is equivalent to full reconstruction within a predefined margin of $0.02$ accuracy on most benchmarks and pooled over the controlled sweep, at exponentially lower cost; deficits of $0.02$-$0.04$ remain on the most cross-cut tasks. Fusion tops the dial's accuracy/cost frontier, is more robust to shot and device noise, and loses nothing as the coupled model's entangling depth grows. We state the exact condition under which fusion must lose accuracy, a decision-relevant cross-cut correlator, and realize it with entangled-state inputs; for classical inputs the register partition discards no information. We claim no advantage over classical machine learning.