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.
We plan to examine the behaviour of an interacting CTQW with two walkers. We will examine the interaction of the walkers with noncommuting primitives. A tool for our work will be the possibility to endow such a walk with a notion of trajectory, in the sense of sample path of an associated Markov process.This will provide us with such notions as sojourn time and first passage time as heuristic tools for gaining intuition about the behaviour of the system.