Solving QUBO Problems Using Hybrid Quantum-Classsical Neural Networks

Hybrid quantum–classical architectures such as the Quantum-Classical Encoder–Decoder (QCED) aim to use analog quantum simulators as differentiable activation functions for QUBO optimization. However, Rydberg-based implementations often exhibit parameter saturation, rendering the quantum layer effectively inactive. We identify restricted control parameter ranges as the primary bottleneck and show that relaxing constraints on the global Rabi frequency and local detunings induces a transition to active training dynamics with nonzero gradients. Benchmarks on MaxCut and MWIS demonstrate that the relaxed QCED model learns nontrivial quantum mappings and achieves improved solution quality over classical baselines, highlighting the trade-off between experimental constraints and expressive quantum control.