How to test the “quantumness” of a quantum computer?
I posted this question in the forum of IBM quantum Experience web site :
How to test the “quantumness” of a quantum computer?
As Quantum computer would be first accessible via the Cloud, I wonder if there are existing tips & tric to test the “quantumness” of my programs and if they really run on a real Quantum hardware and not a simulator…
Seems to be an attractive and shared interest with the community has the statistic of the post are quit important
What the community told us

I noted the terminology of one guy : is like a “turing test” for a quantum computer 🙂

We have to create nonclassical states, for example entangled states and perform measurements to show that these states are not behaving classically. There are examples of this in the tutorial.

The standard way to test the quantumness of a general system is to carry out the Bell test (see section III.4 in the Library)

You only need to do the Bell test for a large enough system, then no classical simulator can compete in preparing the entangled state of >50 qubits

you could try to do some sort of integer randomness test with outputs from a thoruoughly entangled code?

The other way to verify ‘quantumness’ is to run a sequence of a hard algorithm, where every next iteration is double the problem size of the previous iteration. If you see the running time only increase linearly then you have an indication the hardware is indeed using quantum resources.

I don’t believe you can, practically speaking. They already have an ideal simulation of it, the difference between a simulation of something and the real thing is the error involved

Although, the idea proposed by simon_yin of doubling the problem size for each next iteration could work. Nice discussion!

your answer is almost perfect, but quantumness is not about “randomness”, is about “correlations”, “tunneling” and other features.

Classical systems can be random, while we do not forget the deterministic nature of quantum computing –you beforehand know all the resulting matrices in a product (and time evolution is unitary until measuring the whole quantum system). The error of measurements is not the guide we need, so noise isn’t a clue as important as we can think. The pattern of quantum results is what makes sense to classify them apart from classical systems outcomes. Randomness is the preferred feature of cheap books about “quantum and sciences”, but written from an amateur sight (closer to journalists than to scientists). If I’m wrong, Bernoulli family should have been awaiting Planck’s birth to develop the mathematical statistics, joining forces with Chebyshev, Laplace and other thinkers.

I guess I was not clear. I realize that the unitary evolution of an initial quantum state is deterministic up to the point of measurement. But randomness occurs at the point of measurement.
Finally IBM guys answer with their proposal :
Hi @yannallain this is a hard question. The method we like is the quantum volume. Check out @levsbishop video here for a brief overview. There is a technical white paper that can be found here.
Source of all detailed discussion