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

TL;DR

This paper investigates the error thresholds and resource costs for fault-tolerant quantum computing using Majorana fermions combined with unprotected quantum systems, highlighting conditions for improved efficiency.

Contribution

It analyzes the error correction performance in hybrid topological quantum systems and identifies when Majorana fermions can reduce resource requirements.

Findings

Error correction performance depends on noise susceptibility of Majorana fermions.

High fault-tolerance threshold achievable if topological charge is noise-insensitive.

Potential to encode logical qubits with significantly fewer physical qubits.

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.