Is this a convex problem with respect to x? How to write this constraint in cvx?

You should be telling is, not asking us, whether a problem is convex, And asking for help in entering in CVX only if it is convex,

I don’t know what the notation, conventions, and assumptions are, but it doesn’t look convex to me (`-2^x`

in a matrix being constrained to be psd looks rather non-convex) . It doesn’t even look like the matrix being constrained to be psd is even necessarily symmetric. You presumably understand what the notation, conventions, and assumptions are; so you will have to see if somehow there is a reforrmulation (for instance change of variables) which makes it convex.