Permutation-invariant codes encoding more than one qubit

TL;DR

This paper develops permutation-invariant quantum codes that encode multiple qubits and effectively suppress dominant spontaneous decay errors, combining elementary number theory with quantum error correction principles.

Contribution

It introduces new permutation-invariant codes capable of encoding more qubits while reducing leading order spontaneous decay errors, advancing quantum error correction techniques.

Findings

Codes encode increasing quantum information

Effective suppression of spontaneous decay errors

Utilizes elementary number theory in code construction

Abstract

A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation invariant codes and quantum error correction.