Quantum Simulations with Rydberg Atoms
Following Feynman and as elaborated on by Lloyd, a universal quantum simulator (UQS) is a controlled quantum device which efficiently reproduces the dynamics of any other many particle quantum system with short range interactions. These dynamics can refer to both coherent Hamiltonian and dissipative open system evolution. Here we show that laser excited Rydberg atoms in large spacing optical or magnetic lattices provide an efficient implementation of a UQS for spin models involving (high order)n-body interactions. This includes the simulation of Hamiltonians of exotic spin models involving n-particle constraints such a the Kitaev toric code, color code, and string nets. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key basic building block of our architecture is efficient and high-fidelity n-qubit entangling gates via auxiliary Rydberg atoms, including a possible dissipative time step via optical pumping. This allows to mimic the time evolution of the system efficiently by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates.