Pattern formation in quantum Turing machines

We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head [Formula Presented] rotating along a closed Turing tape [Formula Presented] additional pseudospins). The dynamical evolution of the Bloch vector of S, which can be decomposed into [Formula Presented] primitive pure state Turing-head trajectories, gives rise to fascinating geometrical patterns reflecting the entanglement between head and tape. These machines thus provide intuitive examples for quantum parallelism and, at the same time, means for local testing of quantum network dynamics. © 1999 The American Physical Society.