One of the main steps in Hybrid Quantum algorithms for solving Combinatorial Optimization problems is the calculation of the expected value of a hermitian operator $H = \sum{H_i}$ (where $H_i$ are products of Pauli Matrices on a subset of the qubits) constructed from the structure of the optimization function $C(z)$ with respect to some parametrized state $\newcommand{\ket}[1]{\lvert#1\rangle}\ket{\theta}$.
As far as I've read, in practice one of the main procedures in calculating this expectation value is through sampling, where you basically measure $\ket{\theta}$ on the computational basis and use the proportions of observed outcomes as the probability of each solution and then evaluating $C(z)$ on each outcome (https://qiskit.org/textbook/ch-applications/qaoa.html).
Wouldn't this procedure be infeasible when $n$ grows too big? If anyone knows of other alternatives it would be greatly appreciated
