Quantum Computation with Topological Codes: from qubit to topological fault-tolerance

TL;DR

This paper provides a comprehensive review of fault-tolerant topological quantum computation using surface codes, explaining fundamental concepts, models, and interdisciplinary connections in a pedagogical manner.

Contribution

It offers an in-depth, pedagogical overview of topological quantum computation with surface codes, integrating circuit-based and measurement-based models and connecting to other physics fields.

Findings

Clarifies the relation between circuit-based and measurement-based topological models

Explains the use of defects in surface codes for quantum computation

Discusses interdisciplinary links with condensed matter physics and statistical physics

Abstract

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer formalism, and measurement-based quantum computation, are also provided in a pedagogical way. Topological quantum computation by brading the defects on the surface code is explained in both circuit-based and measurement-based models in such a way that their relation is clear. The interdisciplinary connections between quantum error correction codes and subjects in other fields such as topological order in condensed matter physics and spin glass models in statistical physics are also discussed. This manuscript will be appeared in SpringerBriefs.