Pattern formation in quantum Turing machines
Ilki Kim, Günter Mahler · Physical Review A · 1999
We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head $(\mathrm{pseudospin}S)$ rotating along a closed Turing tape $(M$ additional pseudospins). The dynamical 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. These machines thus provide intuitive examples for quantum parallelism and, at the same time, means for local testing of quantum network dynamics.