iders ▁what ▁a ▁theoretical ▁universal ▁quantum ▁computer ▁could ▁accomplish ▁without ▁necessarily ▁account ing ▁for ▁the ▁difficulty ▁of ▁building ▁a ▁physical ▁quantum ▁computer ▁or ▁dealing ▁with ▁de co her ence ▁and ▁noise . ▁Since ▁quantum ▁information ▁is ▁a ▁general ization ▁of ▁classical ▁information , ▁quantum ▁computers ▁can ▁simulate ▁any ▁classical ▁algorithm . ▁ ▁The ▁complexity ▁class ▁B Q P ▁( bounded - error ▁quantum ▁polynomial ▁time ) ▁is ▁the ▁class ▁of ▁decision ▁problems ▁that ▁can ▁be ▁solved ▁in ▁polynomial ▁time ▁by ▁a ▁universal ▁quantum ▁computer . ▁It ▁is ▁related ▁to ▁important ▁classical ▁complexity ▁classes ▁by ▁the ▁hierarchy ▁. ▁Whether ▁any ▁of ▁these ▁contain ments ▁is ▁proper ▁is ▁still ▁an ▁open ▁question . ▁ ▁The ▁difficulty ▁of ▁prov ing ▁what ▁cannot ▁be ▁done ▁with ▁classical ▁computing ▁is ▁a ▁common ▁problem ▁in ▁definit ively ▁demonstr ating ▁quantum ▁supre m acy . ▁Con tr ary ▁to ▁decision ▁problems ▁that ▁require ▁yes ▁or ▁no ▁answers , ▁sampling ▁problems ▁ask ▁for ▁samples ▁from ▁probability ▁distributions . ▁If ▁there ▁is ▁a ▁classical ▁algorithm ▁that ▁can ▁efficiently ▁sample ▁from ▁the ▁output ▁of ▁an ▁arbitrary ▁quantum ▁circuit , ▁the ▁polynomial ▁hierarchy ▁would ▁collapse ▁to ▁the ▁third ▁level , ▁which ▁is ▁considered ▁very ▁unlikely . ▁Bos on ▁sampling ▁is ▁a ▁more ▁specific ▁proposal , ▁the ▁classical ▁hard ness ▁of ▁which ▁depends ▁upon ▁the ▁int ract ability ▁of ▁calculating ▁the ▁permanent ▁of ▁a ▁large ▁matrix ▁with ▁complex ▁entries , ▁which ▁is ▁a ▁# P - complete ▁problem . ▁The ▁arguments ▁used ▁to ▁reach ▁this ▁conclusion ▁have ▁also ▁been ▁extended ▁to ▁I Q P ▁Sam