  In an interacting continuous time quantum walk, while the walker (the cursor)
is moving on a graph, computational primitives (unitary operators associated
with the edges) are applied to ancillary qubits (the register). The model with
one walker was originally proposed by R. Feynman, who thus anticipated many
features of the Continuous Time Quantum Walk (CTWQ) computing paradigm. In this
note we examine the behaviour of an interacting CTQW with two walkers and
examine the interaction of the walkers with noncommuting primitives. We endow
such a walk with a notion of trajectory, in the sense of sample path of an
associated Markov process, in order to use such notions as sojourn time and
first passage time as heuristic tools for gaining intuition about its
behaviour.
