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

Abstract: A key use of near-term quantum computers is as analogue simulators, matching the action of some virtual or abstracted system onto a program executed on physical quantum hardware. This work explores continuous-time quantum walks (CTQW) on constrained graphs of independent set configurations and implements these abstract walks on analog-mode neutral-atom hardware. First, we explore variational state preparation protocols with limited controls through the lens of CTQW and optimal control to prepare nontrivial target states in non-separable Hilbert spaces. Next, we match these virtual walk dynamics to physical execution on analog-mode neutral atom hardware by leveraging the Rydberg blockade phenomenon. We analyze the convergence and scaling in the preparation of these known states as an indicator of the upper bounds on the quantum speedup mechanisms predicted by ideal CTQWs, showing that these signatures persist even when executed on noisy hardware. Finally, we introduce noise mitigation methods using Bayesian postprocessing. This paper demonstrates the ability to prepare nontrivial entangled states using quantum walks in constrained subspaces, and that nonequilibrium dynamics on constrained independent set supspaces is feasible on cloud-accessible analog-mode neutral-atom quantum computers.