We just entered a fundamental new epoch in computing. Maybe. Google scientists said we did. Then their declaration mysteriously vanished.

Last week, a scientific paper by Google and affiliated researchers was uploaded on a NASA website. Its contents – if legitimate – are not insignificant. In the paper, the scientists claim that quantum processors have "reached the regime of quantum supremacy".

That's a hugely important claim, if it's true; a pivotal milestone in quantum computing, ushering in a sort of regime change in the era of computer science.

But before we get too ahead of ourselves – and explain specifically why this is a big deal – a brief disclaimer: the reason we can't be sure of the paper's legitimacy is that shortly after the research article was uploaded, it was withdrawn for reasons unknown.

The news was originally broken by the Financial Times, which reported both seeing the paper and also that it was subsequently taken down.

(The internet being the internet, though, numerous insta-copies were made before the puzzling deletion, and are now freely available to read online.)

Despite the appearance, disappearance, and reappearance of this provocative paper, Google has not officially explained to anybody what's going on, sparking no end of speculation online about what has or hasn't happened. In that sense, it's a little bit like a mini quantum paradox in itself.

Assuming the paper is for real, though – what is quantum supremacy, and why is this important?

Despite the incredible promise of quantum computers, their potential remains largely theoretical, even to this day. Hypothetically speaking, though, in the future, it's predicted that quantum computers will be able to solve problems that are beyond the reach of the classical computers we use today.

Passing such a threshold will be considered proof of 'quantum supremacy'.

"Demonstrating quantum supremacy – that is, demonstrating a quantum computation that cannot be performed on any conventional computer, even the world's best supercomputer – will be a key milestone in demonstrating that quantum computers have the potential to be very powerful, and hopefully very useful," quantum information theorist Stephen Bartlett told ScienceAlert.

Bartlett, who teaches courses in quantum physics and quantum computing at the University of Sydney, isn't involved with Google's quantum research team, and wouldn't comment on the seemingly leaked paper – which may not be finished research, he noted.

But Bartlett did say the research community was anticipating a Google announcement on this in the very near future.

"It is widely believed that quantum supremacy is 'within reach' of the latest generation of quantum devices being built, by Google as well as other companies and universities," Bartlett said.

"Google has been quite vocal publicly in their goals to achieve quantum supremacy."

That vocal stance has hit a whole new level, if the purported research paper is to be believed.

In the paper, the authors claim to have developed an experimental quantum processor called 'Sycamore', which has 53 functional qubits and takes about 200 seconds to solve a particular computational problem.

As part of the experiment, a state-of-the-art supercomputer required approximately 10,000 years to perform the same task.

"This dramatic speedup relative to all known classical algorithms provides an experimental realisation of quantum supremacy on a computational task and heralds the advent of a much-anticipated computing paradigm," the authors write.

"To our knowledge, this experiment marks the first computation that can only be performed on a quantum processor. Quantum processors have thus reached the regime of quantum supremacy."

Again, we can't be entirely sure of the paper's veracity, and even if the research is real (which it certainly looks to be), it may not have yet undergone the necessary peer review to substantiate these kinds of claims.

If the claims prove to be true, Bartlett says there may be broader questions of whether demonstrations like this of quantum supremacy, along the lines of what Google has long been advocating, are really the final word.

"While we believe that some quantum computations will be out of reach of any conventional computer, it is a challenge to argue that any particular set of processes cannot be simulated through some suitable trick," Bartlett told ScienceAlert.

"I suspect that the first claims of quantum supremacy will be followed by a lengthy period of contention, where scientists push the limits of conventional supercomputers to find a way to simulate these claimed demonstrations."

In other words, figuring out ways to rigorously test quantum supremacy could be a supreme challenge in itself.

And even when we objectively pass the quantum supremacy threshold, it may take a long time for quantum computers to become as useful to people as conventional computers, especially since quantum computers have significant technological hurdles that need to be refined.

For quantum computing researcher Steven Flammia, also from the University of Sydney, ongoing improvements in the areas of quantum error correction and fault tolerance are just as important, if not more important, than theoretical attempts to reach supremacy.

"In my mind, those are sort of more significant than this initial quantum supremacy announcement," Flammia told ScienceAlert.

"Once you can achieve error correction and fault tolerance, there's a very strong theoretical reason to believe that there are no 'in principle' obstacles to scaling up large scale useful quantum computation."

When these technologies mature, and quantum supremacy is assured, Bartlett says quantum computers should be able to solve a wide range of problems that are fundamental to modern life.

"Key areas of interest include drug design, developing new high-tech materials, and big implications for information security," Bartlett says.

Within five years, even, it's possible quantum computers will be making meaningful strides in areas of academic research, Flammia thinks, adding that the emerging computational abilities could start helping us to design things like high-temperature superconductors, or better understand the process of nitrogen fixation.

"Those baby steps could be useful to us academics within five years," Flammia says. "I think it's decades before, you know, you're logging into a quantum laptop."

Cautious timeframes and expectations seem entirely reasonable, but in a world where quantum supremacy may have already dawned (watch this space…), who knows what the limits are?

"With devices that are quantum supreme," Bartlett says, "I think we will see the rise of a new generation of quantum-savvy coders and hackers who find applications of quantum computers everywhere."