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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.