▁application ▁of ▁this ▁is ▁a ▁password ▁cra cker ▁that ▁attempts ▁to ▁guess ▁the ▁password ▁or ▁secret ▁key ▁for ▁an ▁encrypted ▁file ▁or ▁system . ▁Sym metric ▁ci ph ers ▁such ▁as ▁Tri ple ▁DES ▁and ▁A ES ▁are ▁particularly ▁vulner able ▁to ▁this ▁kind ▁of ▁attack . ▁This ▁application ▁of ▁quantum ▁computing ▁is ▁a ▁major ▁interest ▁of ▁government ▁ag encies . ▁ ▁Quant um ▁simulation ▁▁ ▁Since ▁chem istry ▁and ▁nan ote chn ology ▁rely ▁on ▁understanding ▁quantum ▁systems , ▁and ▁such ▁systems ▁are ▁impossible ▁to ▁simulate ▁in ▁an ▁efficient ▁manner ▁class ically , ▁many ▁believe ▁quantum ▁simulation ▁will ▁be ▁one ▁of ▁the ▁most ▁important ▁applications ▁of ▁quantum ▁computing . ▁Quant um ▁simulation ▁could ▁also ▁be ▁used ▁to ▁simulate ▁the ▁behavior ▁of ▁atoms ▁and ▁particles ▁at ▁unusual ▁conditions ▁such ▁as ▁the ▁re actions ▁inside ▁a ▁coll ider . ▁ ▁Quant um ▁an ne aling ▁and ▁ad i ab atic ▁optimization ▁ ▁Quant um ▁an ne aling ▁or ▁Ad i ab atic ▁quantum ▁computation ▁re lies ▁on ▁the ▁ad i ab atic ▁theorem ▁to ▁undert ake ▁calculations . ▁A ▁system ▁is ▁placed ▁in ▁the ▁ground ▁state ▁for ▁a ▁simple ▁Hamiltonian , ▁which ▁is ▁slowly ▁evol ved ▁to ▁a ▁more ▁complicated ▁Hamiltonian ▁whose ▁ground ▁state ▁represents ▁the ▁solution ▁to ▁the ▁problem ▁in ▁question . ▁The ▁ad i ab atic ▁theorem ▁states ▁that ▁if ▁the ▁evolution ▁is ▁slow ▁enough ▁the ▁system ▁will ▁stay ▁in ▁its ▁ground ▁state ▁at ▁all ▁times ▁through ▁the ▁process . ▁ ▁Sol ving ▁linear ▁equations ▁ ▁The ▁Quant um ▁algorithm ▁for ▁linear