Generation of quantum states by the dynamics of spin chains: Analytical solution

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Abstract

We design a quasi-one dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left hand site to any specified single particle state on the whole chain. Our treatment is an exact solution to a problem which has already been addressed in approximate ways. As two important examples, we study the $W$ states and Gaussian states with arbitrary width.