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We investigate extremely rare top quark decays at a future proton-protoncollider with centre-of-mass energy of 100 TeV. We focus on two decay modes:radiative decay with a $Z$ boson, $t \rightarrow b WZ$, and flavour-changingneutral decay with a Higgs boson, $t \rightarrow h c$, the former beingkinematically suppressed with a branching ratio of $\mathcal{O}(10^{-6})$, andthe latter highly loop-suppresed, with a branching ratio of$\mathcal{O}(10^{-15})$. We find that $t \rightarrow b WZ$ will be verychallenging to observe in top quark pair production, even within well-motivatedbeyond-the-Standard Model scenarios. For the mode $t\rightarrow h c$ we find astronger sensitivity than that obtained by any future LHC measurement by atleast one order of magnitude.

Rare top quark decays at a 100 TeV proton-proton collider: $t \rightarrow bWZ$ and $t\rightarrow hc$