Pattern formation in quantum Turing machines

We investigate the iteration of a sequence of local and pair unitary transf ormations, which can be interpreted to result from a Turing-head (pseudospi n S) rotating along a closed Turing tape (M additional pseudospins). The dy namical evolution of the Bloch vector of S, which can be decomposed into 2( M) primitive pure state Turing-head trajectories, gives rise to fascinating geometrical patterns reflecting the entanglement between head and tape. Th ese machines thus provide intuitive examples for quantum parallelism and, a t the same time, means for local testing of quantum network dynamics.