/a/
does not contain a quantifier, but there are an infinite amount of strings it will match. And if you only want to consider anchored strings:
my $q1;
$q1 = qr /a(??{$q1})?/;
my $q2 = qr /^$q1$/;
matches all strings containing nothing but a's. But it doesn't use any of the quantifiers you mentioned.
Also,
/^(?!)*$/
contains a
* quantifier, but it doesn't actually match any string. Perhaps you want to discount lookahead. Then I give you:
/^(|)*$/
It'll give a warning, but all it matches is the empty string. But it does have a
* quantifier.
