  Self-assembled InAs quantum dots (QDs), which have long hole-spin coherence
times and are amenable to optical control schemes, have long been explored as
building blocks for qubit architectures. One such design consists of vertically
stacking two QDs to create a quantum dot molecule (QDM). The two dots can be
resonantly tuned to form "molecule-like" coupled hole states from the
hybridization of hole states otherwise localized in each respective dot.
Furthermore, spin-mixing of the hybridized states in dots offset along their
stacking direction enables qubit rotation to be driven optically, allowing for
an all-optical qubit control scheme. Increasing the magnitude of this spin
mixing is important for optical quantum control protocols. To enhance the
tunnel coupling and spin-mixing across the dots, we introduce Bi in the GaAs
inter-dot barrier. Previously, we showed how to model InAs/GaBiAs in an
atomistic tight-binding formalism, and how the dot energy levels are affected
by the alloy. In this paper, we discuss the lowering of the tunnel barrier,
which results in a three fold increase of hole tunnel coupling strength in the
presence of a 7% alloy. Additionally, we show how an asymmetric strain between
the two dots caused by the alloy shifts the resonance. Finally, we discuss
device geometries for which the introduction of Bi is most advantageous.
