Contstruct $Q$ such as $Q^*A-DQ^* =R$

Question

Let $A$ and $D=\mathrm{diag}\{d_1,\dots,d_n\}$ be $n\times n$ hermitian matrices. Construct unitary matrix $Q$ such as $Q^* A - DQ^* = R$, where $R$ is upper triangular.

Here $Q^*$ is conjugate transpose.