Either use CVX 2.2, with Mosek as solver (preferable), or if that is not possible, install CVXQUAD and its exponential.m replacement, and follow the directions at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .
The scaling of H is very bad, and may make the solution unreliable.Try to improve scaling so that most non-zero input numbers are within a few orders of magntiude of 1. If not using Mosek, you can also try SeDuMi as solver.
After you have done all of the preceding, if the problem is still reported as infeasible, follow the advice at https://yalmip.github.io/debugginginfeasible/ , all of which also applies to CVX, except for section 1.