The infinite-range quantum spin glasses with cubic anisotropy (K) are
studied using a combination of the imaginary-time representation with
the n-replica approach and the thermofield dynamic method. Mean-field
theory phase diagrams in the temperature-anisotropy plane (T,K) are pr
esented for quantum spin numbers S ranging from 2 to 9/2. At T=0, the
ground state is nonmagnetic and the spin-glass order is absent for int
eger spin and large cubic anisotropy, the sign of which depends on S.
For half-integer S and sufficiently low temperatures the spin-glass ph
ase persists for arbitrary K.