A search is presented for the single production of a heavy vector-like quark (B) decaying to a Higgs boson and a bottom quark, $\mathrm{B}\rightarrow\mathrm{H}\mathrm{b}$, with the Higgs boson decaying to a pair of bottom quarks. The decay products of the Higgs boson are highly boosted, hence typically collimated. They are reconstructed as a single, massive jet, with heavy flavour content. The single production of vector-like quarks is characterised by the presence of a light flavour quark emitted in the forward region of the detector. The analysis is performed using a data sample collected in 2016 by the CMS experiment at the LHC in proton-proton collisions at a centre-of-mass energy of \sqrt{s}=13~\mathrm{TeV}, corresponding to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. The observation is consistent with background expectation and upper limits are placed on the production cross section times the branching ratio of a vector-like quark B decaying to a Higgs boson and a bottom quark. Values of cross section times branching ratio above $0.07$--1.28~\mathrm{pb} are excluded at $95\%$ confidence level for masses of $700$--1800~\mathrm{GeV}, assuming a resonance with negligible width with respect to experimental resolution. Similar sensitivity is observed for different assumptions on the intrinsic width of the vector-like quark B.

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