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We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involving many-body interactions and constraints. The central building block of the simulation scheme is constituted by a mesoscopic Rydberg gate that permits the entanglement of several atoms in an efficient, robust and quick protocol. In addition, optical pumping on ancillary atoms provides the dissipative ingredient for engineering the coupling between the system and a tailored environment. As an illustration, we discuss how the simulator enables the simulation of coherent evolution of quantum spin models such as the two-dimensional Heisenberg model and Kitaevs toric code, which involves four-body spin interactions. We moreover show that in principle also the simulation of lattice fermions can be achieved. As an example for controlled dissipative dynamics, we discuss ground state cooling of frustration-free spin Hamiltonians.
Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail. Many platforms are being developed towards this goal, in particular bas
Arrays of optically trapped atoms excited to Rydberg states have recently emerged as a competitive physical platform for quantum simulation and computing, where high-fidelity state preparation and readout, quantum logic gates and controlled quantum d
Digital quantum simulation is a promising application for quantum computers. Their free programmability provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time evolution ope
Quantum simulators could provide an alternative to numerical simulations for understanding minimal models of condensed matter systems in a controlled way. Typically, cold atom systems are used to simulate e.g. Hubbard models. In this paper, we discus
In the last twenty years, Rydberg atoms have become a versatile and much studied system for implementing quantum many-body systems in the framework of quantum computation and quantum simulation. However, even in the absence of coherent evolution Rydb