Engineering Highly Entangled States Using a Rydberg Simulator

Ground states with high entanglement entropy are important in quantum information processing, serving as valuable resources for tasks like quantum computation and error correction. By engineering Hamiltonians that host entangled ground states, the need for complex circuits to generate such entanglement from simpler product states can be bypassed. In general, the entanglement entropy of the ground state of a gapped d-dimensional Hamiltonian is anticipated to adhere to the area law, where the entanglement is non-extensive, scaling instead with the size of the boundary separating subregions. Violations of the area law appear rare in nature, with a notable exception being a class of highly restricted spin Hamiltonians known as Motzkin chains whose ground state corresponds to uniform superpositions of all Motzkin paths. In this talk we report on recent progress on the use of a Rydberg quantum simulator to generate Motzkin-like states and quantify their ground state entanglement. We analyze the corresponding entanglement spectrum in view of the symmetries of the corresponding engineered Hamiltonian. Our results point towards a route to realize highly entangled ground states in an experimentally accessible platform.