Four new fundamental nonlocal quantum computing diagonal operator-state relations are derived which model the interaction between two adjacent atoms of an entangled atomic chain. Each atom possesses four eigen-states. These relations lead to four momentum-space cyclic transformations and are used as the computation states in one-dimensional cellular automaton. Four interacting half-observable periodic planar states appear with the same Poincare cycle. Due to the space-time rotational symmetry of these operator-state relations, a new type of periodic spherical state can be constructed consisting of eight finite space-time quadrants as the special quantum computing result.
Nonlocal quantum computing theory and Poincare cycle in spherical states