  The ferromagnetic and antiferromagnetic nanostructure are crucial for
fundamental spintronics devices, motivated by its potential application in
spintronics, we theoretically investigate the electronic structure of the
ferromagnetic and antiferromagnetic phases of the cylindrical intrinsically
magnetic topological insulator $\mathrm{MnBi_{2}Te_{4}}$ quantum wires for both
cases. We demonstrate that a few surface states exist between the bulk band gap
in the ferromagnetic phase, with only one spin branch. In the antiferromagnetic
phase, we show that three coexistent states exist between the energy gaps of
the quantum wires.
