I have the following quadratic cost function
$$ J(t) = \int_{0}^{t} \left[ z(\tau)^\ast A z(\tau) + w(\tau)^\ast B w(\tau) \right] d(\tau) $$
where $w = -Rz$ and A and B are matrices whose values are known. Moreover, $z$ is a vector containing my continous variables. I want to find $R$ which optimizes the cost function and this $R$ is a matrix of real values.
I have read about several ways on how quantum algorithms can be used for optimization of QUBO by using an adiabatic process where a hamiltonian time evolves into another hamiltonian whose ground state is designed to be the minimum of the cost function.
I have since searched for ways in which my problem can be formalized into a QUBO problem and I have found as mentioned in this paper and in answers to questions along the line of this and this one, that continuous variables need to be binarized to fit in the QUBO description. This ultimately leads to an increase of number of binary variables.
My Question resides in that I do not understand how I can map the output of my QAOA to be the values of the $R$ matrix. To clarify what I mean more accurately, consider the maxcut problem. In the maxcut problem you can think of the output of measurement of each qubit as which node is 1 and which is 0. In case of continuous variable optimization, it is the mapping of the output to the $R$ matrix that is missing from my understanding conceptually and mathematically. Please feel free to correct any incorrect assumptions in my understanding along the way.
