Topological Quantum Computing with p-Wave Superfluid Vortices

TL;DR

This paper proposes a novel topological quantum computing scheme using three Majorana fermions in p-wave superfluids, enabling continuous single-qubit gates and two-qubit operations through braiding and coupling.

Contribution

It introduces a new qubit scheme with three Majorana fermions allowing continuous gate operations, expanding beyond previous two- and four-Majorana schemes.

Findings

Continuous 1-qubit gate operations are achievable via braiding and phase control.

Two-qubit gates are realizable through Majorana coupling.

The scheme enhances the set of quantum gates in topological quantum computing.

Abstract

It is shown that Majorana fermions trapped in three vortices in a p-wave superfluid form a qubit in a topological quantum computing (TQC). Several similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. {\bf 86}, 268 (2001)] and Zhang {\it et al.} [Phys. Rev. Lett. {\bf 99}, 220502 (2007)] have proposed schemes in which a qubit is implemented with two and four Majorana fermions, respectively, where a qubit operation is performed by exchanging the positions of Majorana fermions. The set of gates thus obtained is a discrete subset of the relevant unitary group. We propose, in this paper, a new scheme, where three Majorana fermions form a qubit. We show that continuous 1-qubit gate operations are possible by exchanging the positions of Majorana fermions complemented with dynamical phase change. 2-qubit gates are realized through the use of the coupling between Majorana fermions of different qubits.