Analysis of quantum error correction with symmetric hypergraph states

TL;DR

This paper investigates the limitations of symmetric hypergraph states in quantum error correction, showing they are ineffective for independent errors up to 30 qubits, and explores hypergraph codes for protected qubits.

Contribution

It demonstrates the ineffectiveness of symmetric hypergraph states for independent error correction and generalizes graph codes to hypergraph codes for protected qubits.

Findings

Symmetric hypergraph states are not useful for correcting independent errors up to 30 qubits.

Hypergraph codes can be constructed for error models with protected qubits.

Generalization of known graph codes to hypergraph codes is achieved.

Abstract

Graph states have been used to construct quantum error correction codes for independent errors. Hypergraph states generalize graph states, and symmetric hypergraph states have been shown to allow for the correction of correlated errors. In this paper, it is shown that symmetric hypergraph states are not useful for the correction of independent errors, at least for up to 30 qubits. Furthermore, error correction for error models with protected qubits is explored. A class of known graph codes for this scenario is generalized to hypergraph codes.