How to avoid loops in building CVX constraints

Dear all,
I need to add constraints like this:

trace(Qm*X) >= lm (m=1:3000)

where Qm and X are N by N matrix, lm is a given real number. matrix X is the optimization variable, and Qm and lm are different for each m.

As can be seen, the constraint number are too many, which means using a loop in MATLAB is really time consuming. How can I modify it in an efficient manner?

I would really appreciate any help here.
Thank you in advance.