Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations

Abstract

In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which cannot be simulated with a classical computer due to the exponential increase of the Hilbert space with the size of the system and which cannot be measured or controlled in an actual experiment. The system will interact with the surrounding environment, with the other particles in the system and be implemented using 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 using 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 entangled 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.

Revtex 4-1, 14 pages, 21 figures, version 2 has typos corrected and acknowledgement added

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