We propose a topological qubit in which braiding and readout are mediated by the 4π Majorana-Josephson effect. The braidonium device consists of three Majorana nanowires that come together to make a tri-junction; in order to control the superconducting phase differences at the tri-junction the nanowires are enclosed in a ring made of a conventional superconductor; and in order to perform initialization/readout one of the nanowires is coupled to a fluxonium qubit through a topological Josephson junction. We analyze how flux-based control and readout protocols can be used to demonstrate braiding and qubit operation for realistic materials and circuit parameters.
@article{arxiv.1808.03309,
title = {Braidonium: a braiding quantum circuit based on the $4\pi$ Josephson effect},
author = {John P. T. Stenger and Michael Hatridge and Sergey M. Frolov and David Pekker},
journal= {arXiv preprint arXiv:1808.03309},
year = {2019}
}