Finite cyclic quantum state machines: a topological perspective

Finite cyclic quantum state machines (FCQSMs) are characterized by free act ions of finite cyclic groups upon odd-dimensional spheres. This provides fo r a covering space representation for all such machines. FCQSM simulation, as well as simple, quotient, and split FCQSMs are defined within this conte xt. The notions of dynamical and process symmetries for FCQSMs are introduc ed and it is shown that although all FCQSMs obey a weak version of a FCQSM symmetry principle, only those which adhere to a strong version of this pri nciple can simulate special FCQSMs defined by their dynamical symmetries. F inally, a simulation complexity index and an induced topological complexity index are defined for FCQSMs and an order relation is developed in terms o f these indices which serves as a more precise statement of the weak versio n of the FCQSM symmetry principle. These indices are also shown to be relat ed to FCQSMs which do not conform to the strong version of the FCQSM symmet ry principle.