We present a scalable architecture for fault-tolerant topological quantum
computation using networks of voltage-controlled Majorana Cooper pair boxes,
and topological color codes for error correction. Color codes have a set of
transversal gates which coincides with the set of topologically protected gates
in Majorana-based systems, namely the Clifford gates. In this way, we establish
color codes as providing a natural setting in which advantages offered by
topological hardware can be combined with those arising from topological
error-correcting software for full-fledged fault-tolerant quantum computing. We
provide a complete description of our architecture including the underlying
physical ingredients. We start by showing that in topological superconductor
networks, hexagonal cells can be employed to serve as physical qubits for
universal quantum computation, and present protocols for realizing
topologically protected Clifford gates. These hexagonal cell qubits allow for a
direct implementation of open-boundary color codes with ancilla-free syndrome
readout and logical T-gates via magic state distillation. For concreteness,
we describe how the necessary operations can be implemented using networks of
Majorana Cooper pair boxes, and give a feasibility estimate for error
correction in this architecture. Our approach is motivated by nanowire-based
networks of topological superconductors, but could also be realized in
alternative settings such as quantum Hall-superconductor hybrids.Comment: 24 pages, 24 figure