  We take into account higher derivative R4 corrections in M-theory and
construct quantum black hole and black string solutions in 11 dimensions up to
the next leading order. The quantum black string is stretching along the 11th
direction and the Gregory-Laflamme instability is examined at the quantum
level. Thermodynamics of the boosted quantum black hole and black string are
also discussed. Especially we take the near horizon limit of the quantum black
string and investigate its instability quantitatively.
