Quantum supremacy can be achieved in the near-term with 50 superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.

As of 2018, Google and NASA are testing it:

Google and NASA have an agreement to compare Google 72-qubit quantum Bristlecone chip and possibly near-term follow-up quantum chips against regular supercomputers.

And John Preskill writes about how he coined the term:

In 2012, I proposed the term “quantum supremacy” to describe the point where quantum computers can do things that classical computers can’t, regardless of whether those tasks are useful. Where do we go from here? Naturally, Google and other hardware builders hope to find practical applications for their quantum devices. A much larger quantum computer might help researchers design new materials and chemical compounds or build better tools for machine learning, but a noisy quantum computer with a few 100 qubits might not be capable of anything useful. Still, we have ideas about how to use NISQ computers that we’re eager to try, which might yield better methods for optimization or more accurate physical simulations, but we’re not sure if any of these will pan out. It will be fun to play with NISQ technology to learn more about what it can do. I expect that quantum computers will have a transformative effect on society, but this may still be decades away.

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