Quantum Computation Based on Retarded and Advanced Propagation

Computation is currently seen as a forward propagator that evolves (retards) a completely defined initial vector into a corresponding final vector. Initial and final vectors map the (logical) input and output of a reversible Boolean network respectively, whereas forward propagation maps a one-way propagation of logical implication, from input to output. Conversely, hard NP-complete problems are characterized by a two-way propagation of logical implication from input to output and vice versa, given that both are partly defined from the beginning. Logical implication can be propagated forward and backward in a computation by constructing the gate array corresponding to the entire reversible Boolean network and constraining output bits as well as input bits. The possibility of modeling the physical process undergone by such a network by using a retarded and advanced in time propagation scheme is investigated. PACS numbers: 89.70.+c, 02.50.-r, 03.65.-w, 89.80.+h