Topological Quantum Computing Using Nanowire Devices

TL;DR

This paper simulates Majorana mode exchange in nanowire networks, providing experimental predictions and conditions for topological quantum computing, and proposes a multi-qubit setup for universal, protected quantum operations.

Contribution

It offers the first detailed simulation of Majorana braiding in T-junction nanowires, deriving new adiabatic gating time constraints and a multi-qubit topological quantum computing scheme.

Findings

Gating time must be smaller than inverse squared superconducting gap.

Successful Majorana exchange depends on specific geometric conditions.

Proposed multi-qubit setup enables universal topologically protected quantum computing.

Abstract

The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana states by time-dependently tuning topologically non-trivial parameter regions. In this work, we simulate the exchange of four Majorana modes in T-shaped junctions made out of p-wave superconducting Rashba wires. We derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes. Contrary to the widespread opinion, we show for the first time that in the adiabatic limit the gating time needs to be smaller than the inverse of the squared superconducting order parameter and scales linearly with the gating potential. Further, we show how to circumvent the formation of additional Majorana modes in branched nanowire systems, arising at wire intersection points of narrow junctions. Finally, we propose a multi qubit setup, which allows for universal and in particular topologically protected quantum computing.