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Register a new userHierarchical Majoranas in a Programmable Nanowire Network
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We propose a hierarchical architecture for building logical Majorana zero modes using physical Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three physical Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekule vortex pattern in the set of hybridization amplitudes yields an emergent logical Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, textit{without} moving any of the physical Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such logical Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner.
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