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We numerically compute the low-energy spectrum of a gate-controlledsuperconducting topological nanowire segmented into two islands, eachJosephson-coupled to a bulk superconductor. This device may host two pairs ofMajorana bound states and could provide a platform for testing Majorana fusionrules. We analyze the crossover between (i) a charge-dominated regimeutilizable for initialization and readout of Majorana bound states, (ii) asingle-island regime for dominating inter-island Majorana coupling, (iii) aJosephson-plasmon regime for large coupling to the bulk superconductors, and(iv) a regime of four Majorana bound states allowing for topologicallyprotected Majorana manipulations. From the energy spectrum, we deriveconservative estimates for the time scales of a fusion-rule testing protocolproposed recently [arXiv:1511.05153]. We also analyze the steps needed forbasic Majorana braiding operations in branched nanowire structures.

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