▁ ▁Ad i ab atic ▁quantum ▁computer , ▁based ▁on ▁quantum ▁an ne aling ▁( comput ation ▁decom posed ▁into ▁a ▁slow ▁continuous ▁transformation ▁of ▁an ▁initial ▁Hamiltonian ▁into ▁a ▁final ▁Hamiltonian , ▁whose ▁ground ▁states ▁contain ▁the ▁solution ) ▁ ▁Top ological ▁quantum ▁computer ▁( comput ation ▁decom posed ▁into ▁the ▁bra iding ▁of ▁any ons ▁in ▁a ▁ 2 D ▁lattice ) ▁The ▁quantum ▁T uring ▁machine ▁is ▁theoret ically ▁important ▁but ▁the ▁physical ▁implementation ▁of ▁this ▁model ▁is ▁not ▁feas ible . ▁All ▁four ▁models ▁of ▁computation ▁have ▁been ▁shown ▁to ▁be ▁equivalent ; ▁each ▁can ▁simulate ▁the ▁other ▁with ▁no ▁more ▁than ▁polynomial ▁overhead . ▁ ▁Phys ical ▁realiz ations ▁ ▁For ▁phys ically ▁implementing ▁a ▁quantum ▁computer , ▁many ▁different ▁candidates ▁are ▁being ▁purs ued , ▁among ▁them ▁( dist ingu ished ▁by ▁the ▁physical ▁system ▁used ▁to ▁realize ▁the ▁qu bits ): ▁ ▁Super con duct ing ▁quantum ▁computing ▁( qu bit ▁implemented ▁by ▁the ▁state ▁of ▁small ▁super con duct ing ▁circ uits ▁( Jose ph son ▁j unction s ) ▁Tra pped ▁ion ▁quantum ▁computer ▁( qu bit ▁implemented ▁by ▁the ▁internal ▁state ▁of ▁tra pped ▁ ions ) ▁Opt ical ▁l att ices ▁( qu bit ▁implemented ▁by ▁internal ▁states ▁of ▁neutral ▁atoms ▁tra pped ▁in ▁an ▁optical ▁lattice ) ▁Quant um ▁dot ▁computer , ▁spin - based ▁( e . g . ▁the ▁L oss - Di V inc en zo ▁quantum ▁computer ) ▁( qu bit ▁given ▁by ▁the ▁spin ▁states ▁of