Qudit quantum computation on matrix product states with global symmetry

TL;DR

This paper explores how resource states with symmetry-protected topological order enable universal single-qudit measurement-based quantum computation, linking topological phases with quantum computational capabilities.

Contribution

It introduces new classes of resource states with symmetry properties that facilitate quantum computation, extending the understanding of topological order in quantum information.

Findings

Symmetry protects information propagation in cluster states.

Higher symmetry in AKLT states enables nontrivial quantum gates.

Resource states with specific symmetries are universal for qudit measurement-based quantum computation.

Abstract

Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the 1D qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order.