Continuous-time quantum-walk-based ansätze on neutral-atom hardware

Continuous-time quantum walks offer provable speedups for certain computational problems, yet translating these advantages to near-term hardware remains challenging. We realize variational ans\"atze based on continuous-time quantum walks on an analog neutral-atom processor. For unentangled targets, we derive closed-form expressions for near-optimal control parameters that transfer directly to hardware with minimal calibration. On QuEra's Aquila processor, we observe the superquadratic convergence characteristic of efficient quantum walk algorithms, visible at low circuit depth, with theory predicting stronger speedups as hardware improves. For entangled targets, specifically symmetric superpositions in the Rydberg-blockaded subspace, we introduce an optimization protocol exploiting spectral properties of the walk dynamics. The required evolution timescales inversely with the spectral gap, offering an advantage over adiabatic protocols, whose evolution timescales as the inverse square of the spectral gap. We verify this scaling behavior on Aquila and confirm that the prepared states are coherent superpositions via quench dynamics. Our results establish a practical pathway from abstract quantum walk algorithms to analog quantum processors, demonstrating that the dynamics underlying their potential for superquadratic quantum speedup are accessible on current devices.