A practical phase gate for producing Bell violations in Majorana wires

TL;DR

This paper proposes a practical phase gate for Majorana wires that enables Bell violations, advancing the potential for universal fault-tolerant quantum computation with topologically protected Majorana zero modes.

Contribution

It introduces a new phase gate and measurement scheme for Majorana systems, enabling Bell violations and moving beyond classically simulable Clifford operations.

Findings

Demonstrated measurement of Bell violations in Majorana systems

Proposed a new phase gate compatible with existing Majorana wires

Outlined a feasible experimental setup for future Bell violation tests

Abstract

The Gottesman-Knill theorem holds that operations from the Clifford group, when combined with preparation and detection of qubit states in the computational basis, are insufficient for universal quantum computation. Indeed, any measurement results in such a system could be reproduced within a local hidden variable theory, so that there is no need for a quantum mechanical explanation and therefore no possibility of quantum speedup. Unfortunately, Clifford operations are precisely the ones available through braiding and measurement in systems supporting non-Abelian Majorana zero modes, which are otherwise an excellent candidate for topologically protected quantum computation. In order to move beyond the classically simulable subspace, an additional phase gate is required. This phase gate allows the system to violate the Bell-like CHSH inequality that would constrain a local hidden variable theory. In this article, we both demonstrate the procedure for measuring Bell violations in Majorana systems and introduce a new type of phase gate for the already existing semiconductor-based Majorana wire systems. We conclude with an experimentally feasible schematic combining the two, which should potentially lead to the demonstration of Bell violation in a Majorana experiment in the near future. Our work also naturally leads to a well-defined platform for universal fault-tolerant quantum computation using Majorana zero modes, which we describe.