The notions of symmetry and computational feedback in the paradigm of steady, simultaneous quantum computation

Abstract

Digital computation—i.e., the coherent concatenation of logicalif/then statements—is generally mapped onto the temporal transformation of a physical state. In the alternative paradigm of steady, simultaneous quantum computation, logical concatenations are mapped onto the transformations of a quantum steady state into itself. Such transformations, separated from the time variable and thus freed from the one-way progression of time, can mapcircular logical concatenations. This gives rise to nondeterministic and nonrecursive computation. Toy model Hamiltonians of elementary (steady) computations are given to exemplify the applicability of the paradigm.