  We study a two-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. Substitution sequences are known to underlie aperiodic
structures. We show that parameter inputs \alpha_m described by such sequences
can lead here to a quantum dynamics, intermediate between the regular and the
chaotic variant. Exponential parameter sensitivity characterizing chaotic
quantum Turing machines turns out to be an adequate criterion for induced
quantum chaos in a quantum network.
