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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• Majorana qubits in topological insulator nanoribbon architecture
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• Majorana Fermions in Magnetic Chains
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• Gate-controlled supercurrent in epitaxial Al/InAs nanowires
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• Low-field Topological Threshold in Majorana Double Nanowires
• Optimization of the surface code design for Majorana-based qubits
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• Topological Quantum Computing Using Nanowire Devices
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• Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential
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• Superconducting grid-bus surface code architecture for hole-spin qubits
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• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
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• Coulomb Blockade in Fractional Topological Superconductors
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• Transport properties of Majorana bound states networks in the Coulomb blockade regime
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• Spectroscopic Visualization of a Robust Electronic Response of Semiconducting Nanowires to Deposition of Superconducting Islands
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• Interference and parity blockade in transport through a Majorana box
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