▁sol v able ▁by ▁determin istic ▁classical ▁computers . ▁For ▁instance , ▁integer ▁factor ization ▁and ▁the ▁discrete ▁log arith m ▁problem ▁are ▁known ▁to ▁be ▁in ▁B Q P ▁and ▁are ▁sus pected ▁to ▁be ▁outside ▁of ▁P . ▁On ▁the ▁relationship ▁of ▁B Q P ▁to ▁N P , ▁little ▁is ▁known ▁beyond ▁the ▁fact ▁that ▁some ▁N P ▁problems ▁are ▁in ▁B Q P ▁( integer ▁factor ization ▁and ▁the ▁discrete ▁log arith m ▁problem ▁are ▁both ▁in ▁N P , ▁for ▁example ). ▁It ▁is ▁sus pected ▁that ▁N P B Q P ; ▁that ▁is , ▁it ▁is ▁believed ▁that ▁there ▁are ▁efficiently ▁check able ▁problems ▁that ▁are ▁not ▁efficiently ▁sol v able ▁by ▁a ▁quantum ▁computer . ▁As ▁a ▁direct ▁consequence ▁of ▁this ▁belief , ▁it ▁is ▁also ▁sus pected ▁that ▁B Q P ▁is ▁dis joint ▁from ▁the ▁class ▁of ▁N P - complete ▁problems ▁( if ▁an ▁N P - complete ▁problem ▁were ▁in ▁B Q P , ▁then ▁it ▁follows ▁from ▁N P - hard ness ▁that ▁all ▁problems ▁in ▁N P ▁are ▁in ▁B Q P ). ▁ ▁The ▁relationship ▁of ▁B Q P ▁to ▁the ▁basic ▁classical ▁complexity ▁classes ▁can ▁be ▁summar ized ▁as : ▁ ▁It ▁is ▁also ▁known ▁that ▁B Q P ▁is ▁contained ▁in ▁the ▁complexity ▁class ▁# P ▁( or ▁more ▁precisely ▁in ▁the ▁associated ▁class ▁of ▁decision ▁problems ▁P # P ), ▁which ▁is ▁a ▁subclass ▁of ▁P SP ACE . ▁ ▁It ▁has ▁been ▁spec ulated