A geometric protocol for a robust Majorana magic gate

TL;DR

This paper introduces a geometric protocol to implement the missing $/8$ magic gate in Majorana-based quantum computing, enabling universal quantum gates with topological protection and exponential convergence.

Contribution

It presents a universal, hardware-agnostic geometric protocol for the $/8$ magic gate, completing the set of topologically protected quantum gates.

Findings

Protocol converges exponentially with steps

Does not require fine tuning across physical implementations

Can be extended to arbitrary phase gates

Abstract

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves the missing, so called, $\pi/8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $\pi/8$ is substituted by any $\alpha$.