  Semiconductor quantum dots have proven to be a useful platform for quantum
simulation in the solid state. However, implementing a superconducting coupling
between quantum dots mediated by a Cooper pair has so far suffered from limited
tunability and strong suppression. This has limited applications such as Cooper
pair splitting and quantum dot simulation of topological Kitaev chains. In this
work, we propose how to mediate tunable effective couplings via Andreev bound
states in a semiconductor-superconductor nanowire connecting two quantum dots.
We show that in this way it is possible to individually control both the
coupling mediated by Cooper pairs and by single electrons by changing the
properties of the Andreev bound states with easily accessible experimental
parameters. In addition, the problem of coupling suppression is greatly
mitigated. We also propose how to experimentally extract the coupling strengths
from resonant current in a three-terminal junction. Our proposal will enable
future experiments that have not been possible so far.
