Symmetry protected state of Rydberg atoms as resources for universal measurement-based quantum computation

Rydberg arrays have recently emerged as unique platforms for the simulation of strongly entangled states of matter. Combined with the high degree of control on each individual atoms that these systems offer, Rydberg arrays seem to fulfill all the requirements necessary for the realization of measurement based quantum computation. Two natural questions emerge from this observation: have entangled states allowing for universal measurement base quantum computation been realized? can the measurement driving the quantum computation on these states be efficiently realized in current experimental setups?

In this talk, we will show that the quantum dimer state on the Kagome lattice, recently realized with high fidelity in a Rydberg quantum simulator [Semeghini extit{et al.}, Science 374, 6572 (2021)], offers a sufficient resource for universal measurement-based quantum computations. In particular, we provide an efficient encoding of logical qubits in this state, and give explicit measurement sequences that implement a universal set of gates on these qubits. Since the building blocks of the proposed measurements have already been experimentally implemented, our work highlights one possible path towards promoting Rydberg simulators to universal quantum computers relying on the measurement-based model of quantum computation with currently existing technology.