  Quantum deletions, which are harder to correct than erasure errors, occur in
many realistic settings. It is therefore pertinent to develop quantum coding
schemes for quantum deletion channels. To date, not much is known about which
explicit quantum error correction codes can combat quantum deletions. We note
that {\em any} permutation-invariant quantum code that has a distance of $t+1$
can correct $t$ quantum deletions for any positive integer $t$ in both the
qubit and the qudit setting. Leveraging on coding properties of
permutation-invariant quantum codes under erasure errors, we derive
corresponding coding bounds for permutation-invariant quantum codes under
quantum deletions. We focus our attention on a specific family of $N$-qubit
permutation-invariant quantum codes, which we call shifted gnu codes, and show
that their encoding and decoding algorithms can be performed in $O(N)$ and
$O(N^2)$.
