  We study the percolation of a quantum particle on quasicrystal lattices and
compare it with the square lattice. For our study, we have considered
quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and
the octagonally symmetric Ammann-Beenker tiling. The dynamics of the quantum
particle is modelled using continuous-time quantum walk (CTQW) formalism. We
present a comparison of the behaviour of the CTQW on the two aperiodic
quasicrystal lattices and the square lattice when all the vertices are
connected and when disorder is introduced in the form of disconnections between
the vertices. Unlike on a square lattice, we see a significant fraction of
quantum state localised around the origin in quasicrystal lattice. With
increase in disorder, the percolation probability of a particle on a
quasicrystal lattice decreases significantly faster when compared to the square
lattice. This study sheds light on the minimum fraction of disconnections
allowed to see percolation of quantum particle on these quasicrystal lattices.
