▁of ▁problems ▁with ▁respect ▁to ▁quantum ▁computers ▁is ▁known ▁as ▁quantum ▁complexity ▁theory . ▁ ▁Quant um ▁operations ▁▁ ▁The ▁prev ail ing ▁model ▁of ▁quantum ▁computation ▁describes ▁the ▁computation ▁in ▁terms ▁of ▁a ▁network ▁of ▁quantum ▁logic ▁gates . ▁ ▁A ▁memory ▁consisting ▁of ▁ ▁bits ▁of ▁information ▁has ▁ ▁possible ▁states . ▁A ▁vector ▁representing ▁all ▁memory ▁states ▁thus ▁has ▁ ▁entries ▁( one ▁for ▁each ▁state ). ▁This ▁vector ▁is ▁viewed ▁as ▁a ▁probability ▁vector ▁and ▁represents ▁the ▁fact ▁that ▁the ▁memory ▁is ▁to ▁be ▁found ▁in ▁a ▁particular ▁state . ▁ ▁In ▁the ▁classical ▁view , ▁one ▁entry ▁would ▁have ▁a ▁value ▁of ▁ 1 ▁( i . e . ▁a ▁ 1 0 0 % ▁probability ▁of ▁being ▁in ▁this ▁state ) ▁and ▁all ▁other ▁entries ▁would ▁be ▁zero . ▁▁ ▁In ▁quantum ▁mechan ics , ▁probability ▁vectors ▁are ▁generalized ▁to ▁density ▁operators . ▁This ▁is ▁the ▁techn ically ▁rig orous ▁mathematical ▁foundation ▁for ▁quantum ▁logic ▁gates , ▁but ▁the ▁intermediate ▁quantum ▁state ▁vector ▁formal ism ▁is ▁usually ▁introduced ▁first ▁because ▁it ▁is ▁concept ually ▁simpler . ▁This ▁article ▁focus es ▁on ▁the ▁quantum ▁state ▁vector ▁formal ism ▁for ▁simplicity . ▁ ▁We ▁begin ▁by ▁considering ▁a ▁simple ▁memory ▁consisting ▁of ▁only ▁one ▁bit . ▁This ▁memory ▁may ▁be ▁found ▁in ▁one ▁of ▁two ▁states : ▁the ▁zero ▁state ▁or ▁the ▁one ▁state . ▁We ▁may ▁represent ▁the ▁state ▁of ▁this ▁memory ▁using ▁Di rac ▁notation ▁so ▁that ▁ ▁A ▁quantum ▁memory ▁may ▁then ▁be ▁found ▁in ▁any