  Recently, lithographic quantum dots in strained-Ge/SiGe have become a
promising candidate for quantum computation, with a remarkably quick
progression from demonstration of a quantum dot to qubit logic demonstrations.
Here we present a measurement of the out-of-plane $g$-factor for single-hole
quantum dots in this material. As this is a single-hole measurement, this is
the first experimental result that avoids the strong orbital effects present in
the out-of-plane configuration. In addition to verifying the expected
$g$-factor anisotropy between in-plane and out-of-plane magnetic ($B$)-fields,
variations in the $g$-factor dependent on the occupation of the quantum dot are
observed. These results are in good agreement with calculations of the
$g$-factor using the heavy- and light-hole spaces of the Luttinger Hamiltonian,
especially the first two holes, showing a strong spin-orbit coupling and
suggesting dramatic $g$-factor tunability through both the $B$-field and the
charge state.
