Quantum simulation of interacting high-dimensional systems: The influence of noise

We consider the simulation of interacting high-dimensional systems using pairwise interacting qubits. The main tool in this context is the generation of effective many-body interactions, and we examine a number of different protocols for obtaining them. These methods include the usage of higher-order processes (commutator method), unitary conjugation or graph state encoding, as well as teleportation-based approaches. We illustrate and compare these methods in detail and analyze the time cost for simulation. In the second part of the paper, we investigate the influence of noise on the simulation process. We concentrate on errors in the interaction Hamiltonians and consider two generic noise models: (i) timing errors in pairwise interactions and (ii) noisy pairwise interactions described by Master equations of Lindblad form. We analyze and compare the effect of noise for the different simulation methods and propose a way to significantly reduce the influence of noise by making use of entanglement purification together with a teleportation-based protocol.