16 qubits? How hard is it to simulate those 16 qubits with a regular computer? I get this is marketing but people would be better off just running a simulator at this point.
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.
It's pretty easy. If your computer has enough ram to store a size 2^16 length complex vector (which is 2^20 bytes, or 1MB) than you can open up an ipython notebook and write code to apply quantum gates to it with no problem.
The problems start to set in if your RAM can't hold the wavefunction in memory (so around 28 qubits, which takes 2^32 bytes = 4GB of RAM.)
With specialized code and supercomputers you can get a little farther, but you will be fighting exponential growth, so not too much. The practical limit for classical computers is in the 40-50 qubit range.
