  We study a special inhomogeneous quantum network consisting of a ring of $M$
pseudo-spins (here $M = 4$) sequentially coupled to one and the same central
spin under the influence of given pulse sequences (quantum gate operations).
This architecture could be visualized as a quantum Turing machine with a cyclic
``tape''. Rather than input-output-relations we investigate the resulting
process, i.e. the correlation between one- and two-point expectation values
(``correlations'') over various time-steps. The resulting spatio-temporal
pattern exhibits many non-classical features including Zeno-effects, violation
of temporal Bell-inequalities, and quantum parallelism. Due to the strange web
of correlations being built-up, specific measurement outcomes for the tape may
refer to one or several preparation histories of the head. Specific families of
correlation functions are more stable with respect to dissipation than the
total wave-function.
