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The idea of topological quantum computation (TQC) is to store and manipulatequantum information in an intrinsically fault-tolerant manner by utilizing thephysics of topologically ordered phases of matter. Currently, one of the mostpromising platforms for a topological qubit is in terms of Majorana fermionzero modes (MZMs) in spin-orbit coupled superconducting nanowires. However, thetopologically robust operations that are possible with MZMs can be efficientlysimulated on a classical computer and are therefore not sufficient forrealizing a universal gate set for TQC. Here, we show that an array of coupledsemiconductor-superconductor nanowires with MZM edge states can be used torealize a more sophisticated type of non-Abelian defect: a genon in an Ising$\times$ Ising topological state. This leads to a possible implementation ofthe missing topologically protected $\pi/8$ phase gate and thus universal TQCbased on semiconductor-superconductor nanowire technology. We provide detailednumerical estimates of the relevant energy scales, which we show to lie withinaccessible ranges.

Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana Nanowires