Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks

摘要

We present a scalable architecture for fault-tolerant topological quantumcomputation using networks of voltage-controlled Majorana Cooper pair boxes,and topological color codes for error correction. Color codes have a set oftransversal gates which coincides with the set of topologically protected gatesin Majorana-based systems, namely the Clifford gates. In this way, we establishcolor codes as providing a natural setting in which advantages offered bytopological hardware can be combined with those arising from topologicalerror-correcting software for full-fledged fault-tolerant quantum computing. Weprovide a complete description of our architecture including the underlyingphysical ingredients. We start by showing that in topological superconductornetworks, hexagonal cells can be employed to serve as physical qubits foruniversal quantum computation, and present protocols for realizingtopologically protected Clifford gates. These hexagonal cell qubits allow for adirect implementation of open-boundary color codes with ancilla-free syndromereadout and logical $T$-gates via magic state distillation. For concreteness,we describe how the necessary operations can be implemented using networks ofMajorana Cooper pair boxes, and give a feasibility estimate for errorcorrection in this architecture. Our approach is motivated by nanowire-basednetworks of topological superconductors, but could also be realized inalternative settings such as quantum Hall-superconductor hybrids.