Roadmap to Majorana surface codes

Surface codes offer a very promising avenue towards fault-tolerant quantum computation. We argue that two-dimensional interacting networks of Majorana bound states in topological superconductor/semiconductor heterostructures hold several key advantages in that direction, concerning both the hardware realization and the actual operation of the code. We here discuss how topologically protected logical qubits in this Majorana surface code architecture can be defined, initialized, manipulated, and read out. All physical ingredients needed to implement these operations are routinely used in topologically trivial quantum devices. By means of quantum interference terms in linear conductance measurements, single-electron pumping protocols, and gate-tunable tunnel barriers, the full set of quantum gates required for universal quantum computation can be achieved. In particular, we show that designated multistep pumping sequences via tunnel-coupled quantum dots realize high-fidelity ancilla states for phase gates.