Universal quantum computation on a semiconductor quantum wire network

TL;DR

This paper proposes a method for universal quantum computation using a semiconductor quantum wire network near an s-wave superconductor, combining topologically protected and unprotected gates to achieve high error thresholds.

Contribution

It introduces a novel approach to realize universal quantum computation on quantum wire networks by constructing topologically protected two-qubit gates and unprotected single-qubit gates, overcoming previous limitations.

Findings

Achieves a high error threshold of 0.14 for quantum computation.

Constructs topologically protected two-qubit gates.

Enables arbitrary single-qubit phase gates.

Abstract

Universal quantum computation (UQC) using Majorana fermions on a 2D topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include \emph{any} two-qubit gate and also the single-qubit $\pi/8$ phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, \emph{etc.}), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an $s$-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of $0.14$ as compared to $10^{-3}$ to $10^{-4}$ in ordinary unprotected quantum computation.