  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.
