With 16 qubits, the Hilbert space has 2^16 = 65536 elements. For numerical simulation, you need to store the wavefunction amplitude for each of these elements, usually using a double-precision complex number (16 bytes). Altogether the wavefunction can be stored as a vector with 1 MiB of data. AFAIK all quantum computing algorithms can be expressed as a sequence of 1- and 2-qubit operations, which would be implemented as sparse matrix-vector products. So the simulation part is almost trivial. ;) I'd say that for 16 qubits, designing the quantum circuit to perform an actually useful operation is the far more difficult part.

However, once you start adding more qubits the simulation part becomes hard to infeasible. I think I saw some paper which simulated around 40 qubits. Here the wavefunction already needs 16 TiB, so you need a big HPC cluster to run that.