Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires

TL;DR

This paper numerically analyzes a superconducting nanowire device segmented into two islands to explore Majorana bound states, their manipulation, and the associated time scales for fusion and braiding operations, relevant for topological quantum computing.

Contribution

It provides a detailed numerical study of energy spectra and time scales for Majorana manipulation in a segmented nanowire device, including fusion and braiding protocols.

Findings

Identifies regimes for Majorana initialization, coupling, and manipulation.

Estimates time scales for Majorana fusion-rule testing.

Analyzes steps for Majorana braiding in nanowire networks.

Abstract

We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently [arXiv:1511.05153]. We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures.