▁a ▁T uring ▁machine . ▁In ▁other ▁words , ▁quantum ▁computers ▁provide ▁no ▁additional ▁power ▁over ▁classical ▁computers ▁in ▁terms ▁of ▁comput ability . ▁This ▁means ▁that ▁quantum ▁computers ▁cannot ▁solve ▁und ec id able ▁problems ▁like ▁the ▁hal ting ▁problem ▁and ▁the ▁existence ▁of ▁quantum ▁computers ▁does ▁not ▁dis pro ve ▁the ▁Church – T uring ▁th esis . ▁ ▁As ▁of ▁yet , ▁quantum ▁computers ▁do ▁not ▁satisfy ▁the ▁strong ▁Church ▁th esis . ▁While ▁hypoth et ical ▁machines ▁have ▁been ▁realized , ▁these ▁machines ▁cannot ▁be ▁constructed ▁in ▁reality . ▁The ▁strong ▁version ▁of ▁Church ' s ▁th esis ▁requires ▁these ▁machines ▁to ▁be ▁physical , ▁therefore ▁these ▁hypoth et ical ▁machines ▁cannot ▁represent ▁a ▁quantum ▁computer ▁that ▁satisfies ▁the ▁strong ▁Church ▁th esis . ▁ ▁Quant um ▁complexity ▁theory ▁ ▁While ▁quantum ▁computers ▁cannot ▁solve ▁any ▁problems ▁that ▁classical ▁computers ▁cannot ▁already ▁solve , ▁it ▁is ▁sus pected ▁that ▁they ▁can ▁solve ▁many ▁problems ▁faster ▁than ▁classical ▁computers . ▁For ▁instance , ▁it ▁is ▁known ▁that ▁quantum ▁computers ▁can ▁efficiently ▁factor ▁integers , ▁while ▁this ▁is ▁not ▁believed ▁to ▁be ▁the ▁case ▁for ▁classical ▁computers . ▁However , ▁the ▁capacity ▁of ▁quantum ▁computers ▁to ▁acceler ate ▁classical ▁algorithms ▁has ▁rig id ▁upper ▁bounds , ▁and ▁the ▁over wh el ming ▁majority ▁of ▁classical ▁calculations ▁cannot ▁be ▁acceler ated ▁by ▁the ▁use ▁of ▁quantum ▁computers . ▁ ▁The ▁class ▁of ▁problems ▁that ▁can ▁be ▁efficiently ▁solved ▁by ▁a ▁quantum ▁computer ▁with ▁bounded ▁error ▁is ▁called ▁B Q P , ▁for