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Fault-tolerant quantum computing in systems composed of both Majoranafermions and topologically unprotected quantum systems, e.g. superconductingcircuits or quantum dots, is studied in this paper. Errors caused bytopologically unprotected quantum systems need to be corrected with errorcorrection schemes, for instance, the surface code. We find that theerror-correction performance of such a hybrid topological quantum computer isnot superior to a normal quantum computer unless the topological charge ofMajorana fermions is insusceptible to noise. If errors changing the topologicalcharge are rare, the fault-tolerance threshold is much higher than thethreshold of a normal quantum computer, and a surface-code logical qubit couldbe encoded in only tens of topological qubits instead of about a thousandnormal qubits.

Noise threshold and resource cost of fault-tolerant quantum computing with Majorana fermions in hybrid systems