A DCP challenge

Hello everyone!
I have the following semidefinite programming problem:

clear; clc;
n = 12;
x = randn (n,1);
A = randn (n,n);
Ax = A*x;

variable g
variable P(n,n) symmetric
minimize g
subject to
quad_form(Ax , P) <= g*quad_form(x , P);
g >= 0;
P == semidefinite(n);

The right-hand side of the first constraint, seems to violate the no-product rule.

Upon running, the following error massage appears:
Disciplined convex programming error:
Invalid quadratic form(s): not a square.

How can I fix the problem?!

You are trying to upper bound a general rational function in many variables (entries of P). That is not convex.