Quantum Error-Correcting Codes for Qudit Amplitude Damping

TL;DR

This paper develops quantum error-correcting codes tailored for amplitude damping channels in qudits, offering larger code dimensions and multi-error correction capabilities for higher-dimensional quantum systems.

Contribution

It introduces new single- and multi-error-correcting quantum codes for amplitude damping channels in qudits, surpassing previous codes in size and extending to qutrit-specific channels.

Findings

Codes have larger dimensions than previous single-error-correcting codes.

Families of multi-error correcting codes are constructed for amplitude damping channels.

Generalizations include error correction for qutrit V and Lambda channels.

Abstract

Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom or energy dissipation of a bosonic system at zero temperature. We discuss quantum error-correcting codes adapted to amplitude damping channels for higher dimensional systems (qudits). For multi-level atoms, we consider a natural kind of decay process, and for bosonic systems,we consider the qudit amplitude damping channel obtained by truncating the Fock basis of the bosonic modes to a certain maximum occupation number. We construct families of single-error-correcting quantum codes that can be used for both cases. Our codes have larger code dimensions than the previously known single-error-correcting codes of the same lengths. Additionally, we present families of multi-error correcting codes for these two channels, as well as generalizations of our construction technique to error-correcting codes for the qutrit $V$ and $\Lambda$ channels.