Roadmap to Majorana surface codes

Abstract

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 distinct advantages in that direction, both concerning 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. In particular, we show that by means of quantum interference terms in linear conductance measurements, composite single-electron pumping protocols, and gate-tunable tunnel barriers, the full set of quantum gates required for universal quantum computation can be implemented.

23 pages, 8 figures

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• Entangling Spins in Double Quantum Dots and Majorana Bound States
• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
• Majorana phase-gate based on the geometric phase
• Transport Signatures of a Majorana Qubit and Read-out-induced Dephasing
• Two-Channel Kondo Physics in a Majorana Island Coupled to a Josephson Junction
• Spectroscopic Visualization of a Robust Electronic Response of Semiconducting Nanowires to Deposition of Superconducting Islands
• Interfacing a topological qubit with a spin qubit in a hybrid quantum system