I got the same error message as you using both CVX 2.1 build 1116 and CVX 3.0beta build 1177. I think this is a CVX bug, perhaps related to Error: inner matrix dimension must agree in cvxprob/eliminate . The good news is that this is a self-contained example (modulo possibly different random numbers, but the same error occurs for several different random number instantiations I tried).

Unfortunately, I haven’t got this part of the answer “The good news is that this is a self-contained example (modulo possibly different random numbers, but the same error occurs for several different random number instantiations I tried).”

Could you please explain which random numbers are you referring to?

I think this problem is the inner initial value of the variable cannot satisfy “Inner matrix dimensions must agree”.
As the Q_p is positive semidefinite, you should set Q_p “semidefinite symmetric complex” instead of " Q_p == hermitian_semidefinite(N_t)", thus the inner initial value of Q_p is a positive semidefinite matrix.
And problem solved!!