  The realization of topological quantum phases of matter remains a key
challenge to condensed matter physics and quantum information science. In this
work, we demonstrate that progress in this direction can be made by combining
concepts of tensor network theory with Majorana device technology. Considering
the topological double semion string-net phase as an example, we exploit the
fact that the representation of topological phases by tensor networks can be
significantly simpler than their description by lattice Hamiltonians. The
building blocks defining the tensor network are tailored to realization via
simple units of capacitively coupled Majorana bound states. In the case under
consideration, this yields a remarkably simple blueprint of a synthetic double
semion string-net, and one may be optimistic that the required device
technology will be available soon. Our results indicate that the implementation
of tensor network structures via mesoscopic quantum devices opens up a powerful
novel avenue toward the realization and quantum simulation of synthetic
topological quantum matter.
