Semiconductor nanowires provide an ideal platform for various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought in contact with a superconductor 1,2 . To fully exploit the potential of non-Abelian anyons for topological quantum computing, they need to be exchanged in a wellcontrolled braiding operation 3-8 . Essential hardware for braiding is a network of singlecrystalline nanowires coupled to superconducting islands. Here, we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks having a predefined number of superconducting islands.Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire "hashtags" reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase coherent system with strong spin-orbit coupling. In addition, a 2 proximity-induced hard superconducting gap is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens new avenues for the realization of epitaxial 3-dimensional quantum device architectures.Majorana Zero Modes (MZMs) are predicted to emerge once a superconductor (SC) is coupled to a semiconductor nanowire (NW) with a strong spin-orbit interaction (SOI) in an external magnetic field 1,2 . InSb NWs are a prime choice for this application due to the large Landé g-factor (~50) and strong Rashba SOI 9 , crucial for realization of MZMs. In addition, InSb nanowires generally show high mobility and ballistic transport [10][11][12] . Indeed, signatures of Majorana zero modes (MZMs) have been detected in hybrid superconductor-semiconductor InSb and InAs NW systems 11,[13][14][15] . Multiple schemes for topological quantum computing based on braiding of MZMs have been reported, all employing hybrid NW networks 3-8 .Top-down fabrication of InSb NW networks is an attractive route towards scalability 16 , however, the large lattice mismatch between InSb and insulating growth substrates limits the crystal quality. An alternative approach is bottom-up synthesis of out-of-plane NW networks which, due to their large surface-to-volume ratio, effectively relieve strain on their sidewalls, enabling the growth of single-crystalline NWs on highly lattice-mismatched substrates [17][18][19] .Recently, different schemes have been reported for merging NWs into networks [20][21][22] .Unfortunately, these structures are either not single-crystalline, due to a mismatch of the crystal structure of the wires with that of the substrate (i.e. hexagonal NWs on a cubic substrate) 22 , or the yield is low due to the limited control over the multiple accessible growth directions (the yield decreases with the number of junctions in the network) 23 ....

Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices.

Topological superconductivity is an exotic state of matter that supports Majorana zero-modes, which have been predicted to occur in the surface states of three-dimensional systems, in the edge states of two-dimensional systems, and in one-dimensional wires. Localized Majorana zero-modes obey non-Abelian exchange statistics, making them interesting building blocks for topological quantum computing. Here, we report superconductivity induced in the edge modes of semiconducting InAs/GaSb quantum wells, a two-dimensional topological insulator. Using superconducting quantum interference we demonstrate gate-tuning between edge-dominated and bulk-dominated regimes of superconducting transport. The edge-dominated regime arises only under conditions of high-bulk resistivity, which we associate with the two-dimensional topological phase. These experiments establish InAs/GaSb as a promising platform for the confinement of Majoranas into localized states, enabling future investigations of non-Abelian statistics.