# Continuous-time quantum walk-based ans\"atze on neutral atom hardware

## TL;DR

This paper demonstrates the first experimental implementation of continuous-time quantum walk-based variational algorithms on neutral-atom hardware, showing super-quadratic convergence and efficient entangled state preparation, paving the way for practical quantum speedups.

## Contribution

It introduces a novel approach to implement quantum walk-based ans"atze on neutral-atom processors with minimal calibration and demonstrates their effectiveness for both unentangled and entangled states.

## Key findings

- First experimental realization of quantum walk-based ans"atze on neutral-atom hardware.
- Observation of super-quadratic convergence at low circuit depth.
- Efficient preparation of symmetric entangled states with spectral gap scaling.

## 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 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. 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.