  The entanglement-assisted stabilizer formalism provides a useful framework
for constructing quantum error-correcting codes (QECC), which can transform
arbitrary classical linear codes into entanglement-assisted quantum error
correcting codes (EAQECCs) by using pre-shared entanglement between the sender
and the receiver. In this paper, we construct five classes of
entanglement-assisted quantum MDS (EAQMDS) codes based on classical MDS codes
by exploiting one or more pre-shared maximally entangled states. We show that
these EAQMDS codes have much larger minimum distance than the standard quantum
MDS (QMDS) codes of the same length, and three classes of these EAQMDS codes
consume only one pair of maximally entangled states.
