this is not an answer, but a demonstration of possibilities.
the code shown in the question doesn't exhibit the described result, namely
that the left angle bracket is larger than the right one.
since the request was for a smaller set of brakets, i've added examples showing
that the shapes used around the q are the smallest default size. to get
smaller ones, one has to go to ridiculous lengths, explicitly specifying a
different (and inappropriate) size.
note that the coding here isn't good style -- never use multiple adjacent
equation environments. and i've also taken liberties with spacing,
since it's not really clear what is wanted.
it has come to my attention (by way of a comment on Increase in bracket sizes due to power symbol) that the
physics package also supports the
\ket notation, and according to
texdoc physics you can apply a
* to suppress automatic sizing (see page 6).