  The superalgebra of $\Z_2^2$-graded supersymmetric quantum mechanics is shown
to be realizable in terms of a single bosonic degree of freedom. Such an
approach is directly inspired by a description of the corresponding
$\Z_2$-graded superalgebra in the framework of a Calogero-Vasiliev algebra or,
more generally, of a generalized deformed oscillator algebra. In the case of
the $\Z_2^2$-graded superalgebra, the central element $Z$ has the property of
distinguishing between degenerate eigenstates of the Hamiltonian.
