A reductionistic approach to quantum computation

Abstract

In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first parts are made independent of each other by assuming that all ``transmissions'' are removed. The overall state would thus become a superposition of tensor products of the eigenstates of the independent parts. Transmissions are restored by projecting off all the tensor products which violate them. This would be performed by particle statistics; the plausibility of this scheme is based on the interpretation of particle statistics as projection. The problem of the satisfiability of a Boolean network is approached in this way. This form of quantum reductionism appears to be able of taming the quantum whole without clipping its richness.