Nayeli Zuniga-Hansen, Yu-Chieh Chi, Mark S. Byrd
In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain useful information about problems of interest which cannot be simulated with a classical computer due to the exponential increase of the Hilbert space with the size of the system and cannot be measured or controlled in an actual experiment. The system will interact with the surrounding environment and with the other particles in the system and be subjected to imperfect controls making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum computing, however the effects of noise in quantum simulations and how to treat them are not completely understood. In this paper we study an existing quantum algorithm for the one dimensional Fano-Anderson model to be simulated in a liquid-state NMR device. We calculate the evolution of different initial states in the original model, and then we add interacting spins to simulate a more realistic situation. We find that states which are entangle with their environment, and sometimes correlated but not necessarily entangled have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.
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http://arxiv.org/abs/1202.6337
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