Permutation-invariant constant-excitation quantum codes for amplitude damping

TL;DR

This paper introduces permutation-invariant constant-excitation quantum codes that correct amplitude damping errors and are immune to mode permutations, leveraging nullspace methods based on integer partitions.

Contribution

It presents a novel class of quantum codes that combine error correction for amplitude damping with permutation invariance within physical systems.

Findings

Codes correct amplitude damping errors effectively

Codes are immune to mode permutations

Construction uses nullspace of matrices based on integer partitions

Abstract

The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors which model photon loss. Although considerable research has been devoted to quantum error correcting codes for amplitude damping, not so much attention has been paid to having these codes simultaneously lie within the decoherence free subspace of their underlying physical system. One common physical system comprises of quantum harmonic oscillators, and constant-excitation quantum codes can be naturally stabilized within them. The purpose of this paper is to give constant-excitation quantum codes that not only correct amplitude damping errors, but are also immune against permutations of their underlying modes. To construct such quantum codes, we use the nullspace of a specially constructed matrix based on integer partitions.