Discovering Higgs boson pair production through rare final states at a 100 TeV collider

We consider Higgs boson pair production at a future proton collider with centre-of-mass energy of 100 TeV, focusing on rare final states that include a bottom-anti-bottom quark pair and multiple isolated leptons: $hh \rightarrow (b\bar{b}) + n \ell + X$, $n = \{2,4\}$, $X = \{ E_T^\mathrm{miss}, \gamma, -\}$. We construct experimental search strategies for observing the process through these channels and make suggestions on the desired requirements for the detector design of the future collider.