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We examine the role of quantum error correction (QEC) in achieving prettygood quantum state transfer over a class of $1$-d spin Hamiltonians. Recastingthe problem of state transfer as one of information transmission over anunderlying quantum channel, we identify an adaptive QEC protocol that achievespretty good state transfer. Using an adaptive recovery and approximate QECcode, we obtain explicit analytical and numerical results for the fidelity oftransfer over ideal and disordered $1$-d Heisenberg chains. In the case of adisordered chain, we study the distribution of the transition amplitude, whichin turn quantifies the stochastic noise in the underlying quantum channel. Ouranalysis helps us to suitably modify the QEC protocol so as to ensure prettygood state transfer for small disorder strengths and indicates a thresholdbeyond which QEC does not help in improving the fidelity of state transfer.

Pretty good state transfer via adaptive quantum error correction