▁quantum ▁super position ▁ ▁of ▁the ▁two ▁classical ▁states ▁ ▁and ▁: ▁ ▁In ▁general , ▁the ▁coefficients ▁ ▁and ▁ ▁are ▁complex ▁numbers . ▁In ▁this ▁scenario , ▁one ▁qu bit ▁of ▁information ▁is ▁said ▁to ▁be ▁encoded ▁into ▁the ▁quantum ▁memory . ▁The ▁state ▁ ▁is ▁not ▁itself ▁a ▁probability ▁vector ▁but ▁can ▁be ▁connected ▁with ▁a ▁probability ▁vector ▁via ▁a ▁measurement ▁operation . ▁If ▁the ▁quantum ▁memory ▁is ▁measured ▁to ▁determine ▁if ▁the ▁state ▁is ▁ ▁or ▁ ▁( this ▁is ▁known ▁as ▁a ▁computational ▁basis ▁measurement ), ▁the ▁zero ▁state ▁would ▁be ▁observed ▁with ▁probability ▁ ▁and ▁the ▁one ▁state ▁with ▁probability ▁. ▁The ▁numbers ▁ ▁and ▁ ▁are ▁called ▁quantum ▁amplit udes . ▁ ▁The ▁state ▁of ▁this ▁one - qu bit ▁quantum ▁memory ▁can ▁be ▁manip ulated ▁by ▁applying ▁quantum ▁logic ▁gates , ▁analog ous ▁to ▁how ▁classical ▁memory ▁can ▁be ▁manip ulated ▁with ▁classical ▁logic ▁gates . ▁One ▁important ▁gate ▁for ▁both ▁classical ▁and ▁quantum ▁computation ▁is ▁the ▁NOT ▁gate , ▁which ▁can ▁be ▁represented ▁by ▁a ▁matrix ▁ ▁Mathemat ically , ▁the ▁application ▁of ▁such ▁a ▁logic ▁gate ▁to ▁a ▁quantum ▁state ▁vector ▁is ▁model led ▁with ▁matrix ▁multiplication . ▁Thus ▁ ▁and ▁. ▁ ▁The ▁mathematics ▁of ▁single ▁qu bit ▁gates ▁can ▁be ▁extended ▁to ▁operate ▁on ▁multi qu bit ▁quantum ▁mem ories ▁in ▁two ▁important ▁ways . ▁One ▁way ▁is ▁simply ▁to ▁select ▁a ▁qu bit ▁and ▁apply ▁that ▁gate ▁to ▁the ▁target ▁qu bit ▁whilst ▁leaving ▁the ▁remainder ▁of ▁the ▁memory ▁una