▁" bounded ▁error , ▁quantum , ▁polynomial ▁time ". ▁More ▁formally , ▁B Q P ▁is ▁the ▁class ▁of ▁problems ▁that ▁can ▁be ▁solved ▁by ▁a ▁polynomial - time ▁quantum ▁T uring ▁machine ▁with ▁error ▁probability ▁of ▁at ▁most ▁ 1 / 3 . ▁As ▁a ▁class ▁of ▁probabil istic ▁problems , ▁B Q P ▁is ▁the ▁quantum ▁counter part ▁to ▁B PP ▁(" bounded ▁error , ▁probabil istic , ▁polynomial ▁time "), ▁the ▁class ▁of ▁problems ▁that ▁can ▁be ▁efficiently ▁solved ▁by ▁probabil istic ▁T uring ▁machines ▁with ▁bounded ▁error . ▁It ▁is ▁known ▁that ▁B PP B Q P ▁and ▁widely ▁sus pected , ▁but ▁not ▁proven , ▁that ▁B Q P B PP , ▁which ▁intuit ively ▁would ▁mean ▁that ▁quantum ▁computers ▁are ▁more ▁powerful ▁than ▁classical ▁computers ▁in ▁terms ▁of ▁time ▁complexity . ▁ ▁The ▁exact ▁relationship ▁of ▁B Q P ▁to ▁P , ▁N P , ▁and ▁P SP ACE ▁is ▁not ▁known . ▁However , ▁it ▁is ▁known ▁that ▁P B Q PP SP ACE ; ▁that ▁is , ▁the ▁class ▁of ▁problems ▁that ▁can ▁be ▁efficiently ▁solved ▁by ▁quantum ▁computers ▁includes ▁all ▁problems ▁that ▁can ▁be ▁efficiently ▁solved ▁by ▁determin istic ▁classical ▁computers ▁but ▁does ▁not ▁include ▁any ▁problems ▁that ▁cannot ▁be ▁solved ▁by ▁classical ▁computers ▁with ▁polynomial ▁space ▁resources . ▁It ▁is ▁further ▁sus pected ▁that ▁B Q P ▁is ▁a ▁strict ▁su pers et ▁of ▁P , ▁meaning ▁there ▁are ▁problems ▁that ▁are ▁efficiently ▁sol v able ▁by ▁quantum ▁computers ▁that ▁are ▁not ▁efficiently