  Quantum geometry on a discrete set means a directed graph with a weight
associated to each arrow defining the quantum metric. However, these `lattice
spacing' weights do not have to be independent of the direction of the arrow.
We use this greater freedom to give a quantum geometric interpretation of
discrete Markov processes with transition probabilities as arrow weights,
namely taking the diffusion form $\partial_+ f=(-\Delta_\theta+ q-p)f$ for the
graph Laplacian $\Delta_\theta$, potential functions $q,p$ built from the
probabilities, and finite difference $\partial_+$ in the time direction.
Motivated by this new point of view, we introduce a `discrete Schroedinger
process' as $\partial_+\psi=\imath(-\Delta+V)\psi$ for the Laplacian associated
to a bimodule connection such that the discrete evolution is unitary. We solve
this explicitly for the 2-state graph, finding a 1-parameter family of such
connections and an induced `generalised Markov process' for $f=|\psi|^2$ in
which there is an additional source current built from $\psi$. We also discuss
our recent work on the quantum geometry of logic in `digital' form over the
field $\Bbb F_2=\{0,1\}$, including de Morgan duality and its possible
generalisations.
