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

Abstract

Continuous-time quantum walks offer provable speedups for certain computational problems, yet translating these advantages to near-term hardware remains challenging. We present the first experimental demonstration of variational ansätze 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. Experiments on QuEra's Aquila processor provide the first observation of the super-quadratic 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 time scales inversely with the spectral gap, offering an advantage over adiabatic protocols that scale to the square of the spectral gap. We demonstrate this scaling behavior on Aquila and verify that the prepared states are coherent superpositions via quench dynamics. This constitutes the first preparation of such symmetric entangled states on neutral-atom hardware. Our results establish a practical pathway from abstract quantum walk algorithms to analog quantum processors, demonstrating that the dynamics underlying their potential for super-quadratic quantum speedup are accessible on current devices.