Let $X$ be a compact Kähler manifold polarized by an ample line bundle $L$. For $k$ big enough, $L^k$ is generated by holomorphic sections which can be used to embed $X$ holomorphically into complex projective space. The philosophy of quantisation is to canonically associate to each “classical” object defined on $X$ a sequence of “quantized” objects defined on the embedded submanifolds. These objects should converge back to the classical objects when $k$ tends to infinity (in the semi-classical limit). Building on earlier work of Wang, Fine, Ma and Marinescu I show how to work out this program for the Laplacian and construct a sequence of self-adjoint operators $D_k$ acting on some finite dimensional vector spaces. In the semi-classical limit the eigenvalues and eigenspaces of $D_k$ converge to those of the Laplacian in an appropriate sense. This opens the route to study of the spectral properties of the Laplacian purely in terms of projective geometry. If time permits we explain how to use these results to quantise the heat flow on $X$. This is joint work with Julien Keller and Reza Seyyedali.