Locality Weak or Strong Anticipation and Quantum Computing. II. Constructivism with Category Theory

The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagrame can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Tirring and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics ,