# Kitaev chain in an alternating quantum dot-Andreev bound state array

**Authors:** Sebastian Miles, David van Driel, Michael Wimmer, Chun-Xiao Liu  
**arXiv:** [2309.15777](https://arxiv.org/abs/2309.15777)  
**Date:** 2023-09-27  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.15777v1/

## Key points

- Proposal of a novel approach to implementing a Kitaev chain using an array of alternating normal and superconductor hybrid quantum dots embedded in semiconductors
- Kitaev chain exhibits topological superconductivity and hosts Majorana zero modes, potential building blocks for fault-tolerant quantum computing
- Key innovation lies in treating the orbitals in the dot and the Andreev bound states in the hybrid on equal footing
- Couplings between low-energy degrees of freedom induced by direct tunneling, simultaneously of both normal and Andreev types
- Tunability of couplings by varying physical parameters such as Zeeman field strength and direction, as well as changing proximity effects on quantum dots
- Possibility to realize different types of Kitaev chains with desired properties through tunability
- Two-site Kitaev chain can be realized using just one normal quantum dot and one hybrid segment
- Scaling up to a three-site Kitaev chain introduces next-nearest-neighbor couplings through high-order tunneling processes
- Energy splitting mitigated when extending the chain towards longer lengths, approaching topological protection
- Larger energy gap obtained from direct tunneling compared to previous methods
- Fewer quantum dots and hybrid segments required compared to conventional designs
- Promising avenue for implementing Kitaev chains using an array of alternating quantum dots and Andreev bound states

## Summary

In this study, the authors propose a novel approach to implementing a Kitaev chain using an array of alternating normal and superconductor hybrid quantum dots embedded in semiconductors. The Kitaev chain is a one-dimensional system that exhibits topological superconductivity and hosts Majorana zero modes, which are potential building blocks for fault-tolerant quantum computing. The key innovation of this proposal lies in treating the orbitals in the dot and the Andreev bound states in the hybrid on equal footing. Both these low-energy degrees of freedom emerge as crucial elements in the Kitaev chain, with their couplings induced by direct tunneling. Importantly, due to the presence of electron and hole components in the Andreev bound state, this coupling is simultaneously of both normal and Andreev types. The authors demonstrate that by varying experimentally accessible physical parameters such as the strength and direction of the Zeeman field, as well as changing proximity effects on the normal quantum dots, it becomes possible to tune the ratio between normal and Andreev couplings. This tunability opens up new possibilities for realizing different types of Kitaev chains with desired properties. One particularly interesting finding is that a two-site Kitaev chain can be realized using just one normal quantum dot and one hybrid segment. Scaling up to a three-site Kitaev chain introduces next-nearest-neighbor couplings through high-order tunneling processes. However, when extending the chain further towards longer lengths, this energy splitting is mitigated, approaching topological protection. This proposed approach offers two immediate advantages over previous methods: Firstly, it allows for obtaining a larger energy gap from direct tunneling; Secondly, it enables creating a Kitaev chain using fewer quantum dots and hybrid segments compared to conventional designs. Overall, this study presents a promising avenue for implementing Kitaev chains using an array of alternating quantum dots and Andreev bound states. The tunability of couplings coupled with potential for achieving topological protection in longer chains make this approach highly relevant for future research into topological superconductivity and quantum computing.