NiO is a prototypical antiferromagnet with a characteristic resonance frequency in the THz range. From atomistic spin dynamics simulations that take into account the crystallographic structure of NiO, and in particular a magnetic anisotropy respecting its symmetry, we describe antiferromagnetic switching at THz frequency by a spin transfer torque mechanism. Sub-picosecond S-state switching between the six allowed stable spin directions is found for reasonably achievable spin currents, like those generated by laser induced ultrafast demagnetization. A simple procedure for picosecond writing of a six-state memory is described, thus opening the possibility to speed up current logic of electronic devices by several orders of magnitude.