Is there an actually functioning quantum computer that to a definite question like "What is two plus two" can give a definite answer like "Four, fullstop"?

I did, but it didn't answer my question. I want to know whether there is an actual physical functioning machine, like the classical one I am writing this on.

The 16-qubit machine has been online for a while. There is now a 20-qubit processor online (which not everyone can access) and the 50-qubit machine is -we are told- in the pipeline (assuming is passes all tests)
This page summarized (in real-time) the status of all the IBM hardware that can currently be accessed via the cloud https://quantumexperience.ng.bluemix.net/qx/devices

Note also that it is expected that both Google and Rigetti Computing will at some point start offering cloud access to their machines.

Btw, since this is probably not apparent to everyone: compare the T1 and T2 times of the 20 qubit machine and the 5 qubit machine; the coherence times of the former are better which is very interesting. They are making progress extremely quickly....

As mentioned, several corporations, including mine, have quantum computers actually in use on practical problems, but I've not seen dramatic success stories to date. I was fortunate to get an in-depth briefing on this technology a couple of years ago.

The idea is that each qubit is in a quantum superposition of logic 0 and logic 1, so each run of an algorithm, involving multiple steps with multiple qubits, yields a solution which is also a superposition of many possible solutions. Presto: parallel processing! Nevertheless, the actual output of each run is only a single number, due to the "projection postulate" (ala von Neumann). So in order to achieve "parallel processing", the same algorithm has to be run many many times, and the ensemble of outputs fall into a statistical distribution per the Born rule. The statistical result can then be viewed as the desired answer.

The biggest obstacle is isolating the qubits from the environment so that they display quantum rather than classical behavior. This is approached using super-cooling, super-conducting, or other techniques. The success metric is the "coherence time", which is the average duration before the pure the quantum state decays due to environmental interaction. Limiting factors include the number of qubits which can be so isolated simultaneously, and the numbers of channels through which each qubit can be logically connected with other qubits without destroying quantum coherence.

What I find interesting is that quantum computers appear to be a practical application of quantum theory, without which they would not work as advertised. This is similar to Navstar GPS which requires relativity, even though some of the engineers didn't believe in it during development.