  Strong spin-orbit semiconductor nanowires coupled to a superconductor are
predicted to host Majorana zero modes. Exchange (braiding) operations of
Majorana modes form the logical gates of a topological quantum computer and
require a network of nanowires. Here, we develop an in-plane selective-area
growth technique for InSb-Al semiconductor-superconductor nanowire networks
with excellent quantum transport properties. Defect-free transport channels in
InSb nanowire networks are realized on insulating, but heavily mismatched InP
substrates by 1) full relaxation of the lattice mismatch at the
nanowire/substrate interface on a (111)B substrate orientation, 2) nucleation
of a complete network from a single nucleation site, which is accomplished by
optimizing the surface diffusion length of the adatoms. Essential quantum
transport phenomena for topological quantum computing are demonstrated in these
structures including phase-coherent transport up to 10 $\mu$m and a hard
superconducting gap accompanied by 2$e$-periodic Coulomb oscillations with an
Al-based Cooper pair island integrated in the nanowire network.
