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

Abstract

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically unprotected quantum systems need to be corrected with error correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer, and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about a thousand normal qubits.

15 pages, 11 figures

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Cited by in corpus (11)

• Roadmap to Majorana surface codes
• Quantum Computing with Majorana Fermion Codes
• Optimization of the surface code design for Majorana-based qubits
• Modeling noise and error correction for Majorana-based quantum computing
• Fault-tolerant fermionic quantum computation based on color code
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Dynamics of quantum resources in regular and Majorana fermion systems
• Edge Modes and Teleportation in a Topologically Insulating Quantum Wire
• Braiding a novel kind of Majorana-like quasiparticles in nanowire quantum dots
• Quantum operation of fermionic systems and process tomography using Majorana fermion gates
• Fault-tolerant fidelity based on few-qubit codes: Parity-check circuits for biased error channels