. ▁ ▁Any ▁quantum ▁computation ▁can ▁be ▁represented ▁as ▁a ▁network ▁of ▁quantum ▁logic ▁gates ▁from ▁a ▁fairly ▁small ▁family ▁of ▁gates . ▁A ▁choice ▁of ▁gate ▁family ▁that ▁enables ▁this ▁construction ▁is ▁known ▁as ▁a ▁universal ▁gate ▁set . ▁One ▁common ▁such ▁set ▁includes ▁all ▁single - qu bit ▁gates ▁as ▁well ▁as ▁the ▁C NOT ▁gate ▁from ▁above . ▁This ▁means ▁any ▁quantum ▁computation ▁can ▁be ▁performed ▁by ▁executing ▁a ▁sequence ▁of ▁single - qu bit ▁gates ▁together ▁with ▁C NOT ▁gates . ▁Though ▁this ▁gate ▁set ▁is ▁infinite , ▁it ▁can ▁be ▁replaced ▁with ▁a ▁finite ▁gate ▁set ▁by ▁appe aling ▁to ▁the ▁Sol ov ay - K ita ev ▁theorem . ▁ ▁Pot ential ▁applications ▁ ▁C rypt ography ▁▁ ▁Integer ▁factor ization , ▁which ▁under p ins ▁the ▁security ▁of ▁public ▁key ▁crypt ographic ▁systems , ▁is ▁believed ▁to ▁be ▁computation ally ▁in fe as ible ▁with ▁an ▁ordinary ▁computer ▁for ▁large ▁integers ▁if ▁they ▁are ▁the ▁product ▁of ▁few ▁prime ▁numbers ▁( e . g ., ▁products ▁of ▁two ▁ 3 0 0 - digit ▁pr imes ). ▁By ▁comparison , ▁a ▁quantum ▁computer ▁could ▁efficiently ▁solve ▁this ▁problem ▁using ▁Sh or ' s ▁algorithm ▁to ▁find ▁its ▁factors . ▁This ▁ability ▁would ▁allow ▁a ▁quantum ▁computer ▁to ▁break ▁many ▁of ▁the ▁crypt ographic ▁systems ▁in ▁use ▁today , ▁in ▁the ▁sense ▁that ▁there ▁would ▁be ▁a ▁polynomial ▁time ▁( in ▁the ▁number ▁of ▁digits ▁of ▁the ▁integer ) ▁algorithm ▁for ▁solving ▁the ▁problem . ▁In ▁particular