Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state

TL;DR

This paper proposes a method for topologically protected quantum gates using non-Abelian anyons in the Pfaffian quantum Hall state, including a protected CNOT and other gates, advancing towards universal quantum computation.

Contribution

It introduces the first topologically protected CNOT gate based on quasihole braidings in the Pfaffian state and extends the set of protected gates towards universality.

Findings

Constructed a topologically protected CNOT gate via quasihole braidings.

Implemented most single-qubit gates except pi/8 braiding.

Proposed protected realizations of Toffoli and Bravyi-Kitaev gates.

Abstract

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected Controlled-NOT gate which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the pi/8 gate, are also explicitly implemented by quasihole braidings. Instead of the pi/8 gate we try to construct a topologically protected Toffoli gate, in terms of the Controlled-phase gate and CNOT or by a braid-group based Controlled-Controlled-Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g_3.