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Self-assembled InAs quantum dots (QDs), which have long hole-spin coherencetimes and are amenable to optical control schemes, have long been explored asbuilding blocks for qubit architectures. One such design consists of verticallystacking two QDs to create a quantum dot molecule (QDM). The two dots can beresonantly tuned to form "molecule-like" coupled hole states from thehybridization of hole states otherwise localized in each respective dot.Furthermore, spin-mixing of the hybridized states in dots offset along theirstacking direction enables qubit rotation to be driven optically, allowing foran all-optical qubit control scheme. Increasing the magnitude of this spinmixing is important for optical quantum control protocols. To enhance thetunnel coupling and spin-mixing across the dots, we introduce Bi in the GaAsinter-dot barrier. Previously, we showed how to model InAs/GaBiAs in anatomistic tight-binding formalism, and how the dot energy levels are affectedby 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 thepresence of a 7% alloy. Additionally, we show how an asymmetric strain betweenthe two dots caused by the alloy shifts the resonance. Finally, we discussdevice geometries for which the introduction of Bi is most advantageous.

Incorporation of random alloy GaBi$_{x}$As$_{1-x}$ barriers in InAs  quantum dot molecules: alloy strain and orbital effects towards enhanced  tunneling