A new video explains the theorem developed at Los Alamos National Laboratory showing that information run through an information scrambler such as a black hole will reach a point where any algorithm will be unable to learn the scrambled data.
“Our theorem implies that we are not going to be able to use quantum machine learning to learn typical random or chaotic processes, such as black holes. In this sense, it places a fundamental limit on the learnability of unknown processes,” said Zoe Holmes (CCS-3, Information Sciences), a post-doc at Los Alamos National Laboratory and coauthor of the paper describing the work published today in Physical Review Letters.
Watch the video for a quick overview of the research from everyone’s favorite quantum explainers, Alice and Bob.
Does a black hole hide all secrets?
In a classic quantum-science thought experiment, Alice throws a book of secrets into a black hole.
Her colleague Bob has a quantum system, such as a quantum computer, that’s entangled with the black hole.
Entanglement is a unique feature of quantum mechanics.
With entanglement, atomic-scale particles are interconnected. Actions performed on one particle similarly affect their entangled partners. That happens even if they’re far apart. And even if some go into a black hole.
The Hayden-Preskill thought experiment says that if Bob has a system entangled with the black hole, he should be able to recover the information from it.
Bob does this by looking at a few particles of light “leaked” by the black hole.
By comparing that to his entangled system, he can figure out how the black hole scrambled Alice’s book. Then he can restore the book.
That would be true even though black holes are a one-way off-ramp from the visible universe. Everything they swallow disappears forever, except those few entangled light particles.
But a new theorem by researchers at Los Alamos National Laboratory says restoring Alice’s book is going to be very difficult or even impossible, after all.
Machine learning stalls on a ‘barren plateau’
The Lab team found that a machine learning algorithm that’s attempting to learn how the black hole scrambles information will stall out on a “barren plateau.”
That means Bob can’t learn what was in Alice’s book.
The Los Alamos theorem puts limits on what quantum algorithms can learn about complex physical systems. Luckily, most physical processes are not as complex as black holes so this doesn't condemn quantum machine learning. But it means we need to carefully pick the problems we apply it to.
Future research may turn up interesting examples of how we could extract complex information from complex systems. There may be situations where the theorem can be evaded. But for now, we are confident that Alice’s secrets are destroyed once she tosses them into a black hole. So she can rest easy that her secrets are safe.
Paper: “Barren plateaus preclude learning scramblers.” Zoe Holmes, Andrew Arrasmith (T-4, Physics of Condensed Matter and Complex Systems), Bin Yan (T-4, Physics of Condensed Matter and Complex Systems), Patrick J. Coles (T-4, Physics of Condensed Matter and Complex Systems), Andreas Albrecht (UC Davis), and Andrew T. Sornborger (CCS-3, Information Sciences). Physical Review Letters. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.190501
Funding: U.S. Department of Energy, Office of Science