Let's decompose what you are doing:

  foreach $id (sort keys %quantum) {
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Okay, so $id contains a string which is also a key in %quantum. Next:

      foreach $date ( sort ... keys %{$quantum{$applid}}) { }
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Okay, now we're going to sort a bunch of keys from a contained hashref. I note that you have $applid instead of $id. Is this a typo, or is this some value imported from elsewhere? Ignoring this fact, your sort looks like:

            sort {   $a->{int(substr($quantum{$id},2,2))} <=> $b->{int
+(substr($quantum{$id},2,2))}
                  || $a->{int(substr($quantum{$id},0,2))} <=> $b->{int
+(substr($quantum{$id},0,2))} }
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The things being fed into your sort (your $a and $b) are the keys (strings), not the values (hash refs). You are trying to dereference the hash keys as hashes and thus your error. You likely meant

foreach my $id (sort keys %quantum) {
    foreach my $date (
            sort {   int(substr($quantum{$id}{$a},2,2)) <=> int(substr
+($quantum{$id}{$b},2,2))
                  || int(substr($quantum{$id}{$a},0,2)) <=> int(substr
+($quantum{$id}{$b},0,2)) } 
            keys %{$quantum{$id}}) {
    }
}
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Or maybe no_slogan guessed better. In either case, see HASHES OF HASHES in perldsc, and maybe perlreftut to boot.

I'm also a little thrown as to why strict is not complaining about you not using my on your loop variables, but that's a different question.