Topological qubits from valence bond solids

TL;DR

This paper constructs topological qubits using $SU(N)$-symmetric valence-bond solid models, demonstrating their topological protection, error-correction properties, and potential for improved quantum coding schemes.

Contribution

It introduces a novel approach to topological qubits based on symmetry-protected topological order in valence-bond solids, including a global twist operation for logical gates.

Findings

Ground state degeneracy due to spontaneous parity symmetry breaking

Topological $Z$-rotation implemented by a global twist operation

Enhanced error-correction properties of symmetry-protected topological order

Abstract

Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with two-fold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical $Z$-rotation by angle $\frac{2\pi}{N}$, for any integer $N > 2$, is provided by a global twist operation, which is of topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.