co her ence ▁time . ▁ ▁As ▁described ▁in ▁the ▁Quant um ▁threshold ▁theorem , ▁if ▁the ▁error ▁rate ▁is ▁small ▁enough , ▁it ▁is ▁thought ▁to ▁be ▁possible ▁to ▁use ▁quantum ▁error ▁correction ▁to ▁suppress ▁errors ▁and ▁de co her ence . ▁This ▁allows ▁the ▁total ▁calculation ▁time ▁to ▁be ▁longer ▁than ▁the ▁de co her ence ▁time ▁if ▁the ▁error ▁correction ▁scheme ▁can ▁correct ▁errors ▁faster ▁than ▁de co her ence ▁introdu ces ▁them . ▁An ▁often ▁c ited ▁figure ▁for ▁the ▁required ▁error ▁rate ▁in ▁each ▁gate ▁for ▁fault - tol er ant ▁computation ▁is ▁ 1 0 − 3 , ▁assuming ▁the ▁noise ▁is ▁dep olar izing . ▁ ▁Me eting ▁this ▁scal ability ▁condition ▁is ▁possible ▁for ▁a ▁wide ▁range ▁of ▁systems . ▁However , ▁the ▁use ▁of ▁error ▁correction ▁brings ▁with ▁it ▁the ▁cost ▁of ▁a ▁greatly ▁increased ▁number ▁of ▁required ▁qu bits . ▁The ▁number ▁required ▁to ▁factor ▁integers ▁using ▁Sh or ' s ▁algorithm ▁is ▁still ▁polynomial , ▁and ▁thought ▁to ▁be ▁between ▁L ▁and ▁L 2 , ▁where ▁L ▁is ▁the ▁number ▁of ▁qu bits ▁in ▁the ▁number ▁to ▁be ▁fact ored ; ▁error ▁correction ▁algorithms ▁would ▁infl ate ▁this ▁figure ▁by ▁an ▁additional ▁factor ▁of ▁L . ▁For ▁a ▁ 1 0 0 0 - bit ▁number , ▁this ▁implies ▁a ▁need ▁for ▁about ▁ 1 0 4 ▁bits ▁without ▁error ▁correction . ▁With ▁error ▁correction , ▁the ▁figure ▁would ▁rise ▁to ▁about ▁ 1 0 7 ▁bits . ▁Comput ation ▁time ▁is