Great question and there are actually quite a few examples. @Remi's answer is actually rather good (not just in jest) because of course we can view all quantum systems as being quantum computers.  Although I'd hazard to say that the Universe doesn't count as being 'predictable' (at least not at the quantum level ;)).  More generally however, any chemical reaction or polarisation experiment is a quantum computation that IS (usually) predictable.

Quantum key distribution via BB84 is an example of the operation of one-qubit quantum computers (used as required), and as we look at ever increasing complexity of quantum computer experiments (multi-qubit ion traps and even liquid-phase NMR) we are definitely seeing small-scale quantum computation.  D-Wave two (as has been mentioned) is still controversial, but I think that the consensus is moving towards this being a working quantum computer, albeit not a conventional circuit-driven quantum computer.

But of course we don't want predictable quantum computers, at least not in the sense of being classically simulable.  Everything mentioned above can be solved classically.  It would appear to be one of complexity and we should be soon able to do computations that are not efficiently classically simulable.

The other big frontier at the moment is boson sampling, which is a form of quantum computation (although not obviously a useful form) which it appears we will very soon be able to solve quantum mechanically and not classically.  Certainly we'll be in the non-classical regime much faster than we will with factorisation or Hamiltonian simulation.

Thanks Andrew, Salva, Mohamed and Remi!

So I get a more certain opinion, that these topics are in big evolution. 

As classical Engineer I search for funtionised realisations. The area is too complex and it's good to find some specialist which are interested in this topics too. I don´t want to live from Quantum Computing, I am interested only in latest news.

Besides I try to give some fundamental needs for a Computer as machine, they will be the same as till now:

a) stearability (human created)

b) controlability (as till now by certain stopable steps or states)

c) predictability (by predefineable Algorithmus) 

My meaning about actual status:

a) Many interesting scientists, many theories coming from Mathematics and Physics, many experiments.

b) no result till now, which we can call a new Quantum Computer till now, we have some circuits and physical experiments on Quantum Level and no usable new Computer on Quantum Level.      

Dear Franz,

Thanks for your clarification.  The fundamental needs you identify are correct, and I would certainly agree with your definition of predictability (with the caveat that of course that a quantum computer showing a quantum speedup should not be efficiently predictable - if we could efficiently predict the outcome classically, we wouldn't need quantum!).

Regarding actual status (b), again, apologies if we degenerate into semantics, but we do have small scale quantum computers such as liquid phase NMR, superconducting circuits, ion traps etc and they are running algorithms.  Of course we do not have the complexity we want yet, nor the number of qubits, or in the case of the D-Wave machine, we don't have general purpose yet.

But perhaps most importantly - the topics are going through 'big evolution' as you say.  It's an exciting time and many of us are convinced that it is simply a matter of 'when quantum' rather than 'if quantum' (or 'why quantum').

Andy

 Dear Franz,

Let me add a little to Andrew's excellent answers. We have by now quite a large number of quantum systems where we can implement small scale quantum computations. These include spin resonance experiments such as NMR, photonic systems, ion and atom traps and superconducting qubits. For each of these systems it is generally possible to run simple quantum algorithms (Grover's algorithm, the Deutsch-Josza algorithm, etc) on a handful of qubits.

So, these systems seem to satisfy your requirements at a very small scale. Every such system has some inaccuracies, even classical computers, but most quantum systems are inherently less stable than classical bits, and pick up errors much quicker. So even for these small scale computations, there is a relatively high error rate, and this is one of the factors limiting the number of qubits. DWave basically plower ahead building devices with many noisy qubits, where as most of the community has gone in the opposite direction, trying to build extremely precise gates and long-lived qubits before scaling up. The big news in recent years is that both superconducting qubits are now near or below the error threshold for fault-tolerance. Although full quantum error correction has not yet been used to extend the life of qubits, this is a development we can expect to see very soon (classical error correction has already been used successfully to extend qubit life, but full quantum error correction is needed to extend beyond the depolarisation time-scale). This is making it a very exciting time to work in the field, since we are starting to see quite rapid experimental progress, particularly in terms of superconducting qubits.

Thanks Andrew and Joseph,

your comments arer realy interesting and realistic true!

While writing my research paper , I personally found quantum theory is exiting but talking realistically we at present have a very less and little knowledge about the subject . As sir franz query is certainly important and every one wants to know ! .

Yes there seems to be no physical realization of real quantum computer , since the nature of qubits is weird (seems to us) , but Dwave published a paper in this regard to clarify there computer to b a quantum computer in reality !  and the clarification related to its idea .I think phenomenons like entanglement , de coherence need to be handled properly to realize a realistic Q computer   (sorry if I am wrong but I m just a beginner)

also I see your question in other view also !

 "Functioning predictable quantum computer "

there isn't a functioning practical realization of a Quantum computer as of yet but Dwave claims to be one  but controversial ! 

Even if a quantum computer is physically realized , it works on probability ( it provides number of answers ) does it mean we still need classical computers after the advent of quantum computers to access the list of probable answers and select the best answer to the problem ?