Shallow and Robust QAOA: Improving Feasibility and Hardware Performance via Linear-Chain and Ramp Schedules

The Quantum Approximate Optimization Algorithm (QAOA) is known to struggle on near-term hardware due to constraint handling, parameter search overhead, and tight depth limits. We address this with a hardware-aware co-design: a linear-ramp parameter schedule paired with a Linear-Chain (LC) ansatz that restricts $ZZ$ interactions to nearest neighbors, lowering swaps and depth. We benchmark Linear-Ramp LC-QAOA against standard QAOA, Two-Step QAOA, and Grover-Mixer QAOA on small VRP instances across ideal simulation, Aer simulation, and IBM Eagle/Heron runs, measuring feasibility, solution quality, and hardware efficiency. Linear-ramp improves convergence and feasibility; LC reduces two-qubit gates and boosts noise robustness. Grover-Mixer and Two-Step can aid constraints in theory but are hampered in practice by deeper circuits. On hardware, overall feasibility remains $<1$\%, yet LC-QAOA with $XpXm$ dynamical decoupling more than doubles feasibility and recovers the optimum in several trials. We also show efficient scaling, including a larger case with ramp-initialized LC-QAOA plus CVaR. The results underscore hardware-aligned ansätze and structured schedules as a promising path.