Foliated Quantum Codes

TL;DR

This paper introduces a method to construct large quantum error-correcting codes from entangled cluster states, enabling foliated quantum error correction with promising performance for quantum communication and computation.

Contribution

It presents a novel construction of foliated quantum codes from CSS codes and provides a generic decoding method, demonstrating effective error correction in turbo codes.

Findings

Turbo codes perform well over moderate depth foliations.

Foliated codes are useful for quantum repeaters.

The construction links cluster states with quantum error correction.

Abstract

We show how to construct a large class of quantum error correcting codes, known as CSS codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error correction codes, and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate CSS codes known as turbo codes, finding that it performs well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation.