Tailoring Many-Body Interactions to Solve Hard Combinatorial Problems

A quantum machine consisting of interacting linear clusters of atoms is proposed for the 3SAT problem. Each cluster with two relevant states of collective motion can be used to register a Boolean variable. Given any 3SAT Boolean formula the interactions among the clusters can be so tailored that the ground state(s) (possibly degenerate) of the whole system encodes the satisfying truth assignment(s) for it. This relates the 3SAT problem to the dynamics of the properly designed glass system.