Benchmarking cluster states built with QuEra neutral atoms

Measurement-based quantum computation proposes to leverage entangled cluster states to perform universal quantum computation. Large scale entanglement is particularly promising within the context of neutral atom systems because atoms have long quantum lifetimes and are readily addressable with currently available optical and microwave technology. But implementation of large-scale, high fidelity cluster states via parallel operations remains an open challenge. The QuEra neutral atom quantum device uses Rydberg interactions to entangle up to 256 atoms at once but, in contrast to digital quantum devices, the QuEra device is an analog quantum device. Furthermore, the only local control is through atom location. We construct a protocol to efficiently generate cluster states in parallel with always-on interactions available with the QuEra device. We also construct a specific, non-local benchmarking procedure based on measurement-based teleportation that uses only global measurements available on the QuEra device. We report benchmarking results for QuEra cluster states that reveal the impact of noise sources, such as atom motion and laser fluctuations. We also explore the role of long-range component of Rydberg interactions. Our work lays the groundwork for scaling up the construction of cluster states using neutral atom systems.