Procedure to tune a three-site artificial Kitaev chain to host Majorana bound states based on transmon measurements

Artificial Kitaev chains (AKCs), formed of quantum dot--superconductor linear arrays, provide a promising platform for hosting Majorana bound states (MBSs) and implementing topological quantum computing. The main challenges along this research direction include the tuning of AKCs for hosting MBSs and the readout of the parity of the chains. In this work, we present a step-by-step procedure for tuning a three-site AKC to its sweet spots based on the spectra of a transmon circuit which is integrated with the chain for the purpose of reading out the parity of the chain. The signatures of the transmon's plasma modes in each step, in particular those related to the appearance of MBSs in the chain, will be given. We find that the sweet spots in a three-site AKC can be classified into three types based on the relative strengths of the elastic cotunneling (ECT) and crossed Andreev reflection (CAR): ECT-dominated sweet spots, genuine sweet spots, and CAR-dominated sweet spots. We show that the ECT-dominated and CAR-dominated sweet spots can be more conveniently accessed and utilized in transmon-based measurements.