Quantum network architecture of tight-binding models with substitution   sequences
  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. 
Ilki Kim, Guenter Mahler