Quantum machine learning reaches its limits: A black hole permanently scrambles irrecoverable information

A new theorem shows that information running through an information scrambler such as a black hole will reach a point where no algorithm will be able to learn the scrambled information.

A black hole permanently scrambles information that no quantum machine learning algorithm can recover, shedding new light on the classic Haydn Preskill thought experiment.

A new theorem in the field of quantum machine learning opens a major hole in our understanding of information scrambling.

"Our theorem means that we won't be able to use quantum machines," said Zoe Holmes, a postdoc at Los Alamos National Laboratory and co-author of the paper published in Physical Review Letters on May 12, 2021. Learning to learn typical random or chaotic processes, such as black holes. In this sense, it is a fundamental limit to the ability to learn unknown processes."

"Thankfully, because most physically interesting processes are simple enough or structured enough that they don't resemble random processes, the results do not condemn quantum machine learning, but highlight understanding its limitations," Holmes said. importance.”

In the classic Hayden-Preskill thought experiment, a fictional Alice throws information, such as books, into a messy black hole. Her companion Bob can still retrieve it using entanglement, a unique feature of quantum physics. But the new work demonstrates that Bob's ability to learn the details of a given black hole's physics is fundamentally limited, meaning it would be very difficult, if not impossible, to reconstruct the information in the book.

"Any information propagating through an information scrambler, such as a black hole, gets to the point where machine learning algorithms stall on a barren plateau, becoming impossible," said Andrew Thornborg, a Los Alamos computer scientist and co-author of the paper. training. That means the algorithm cannot learn the scrambling process." Thornberg is director of the Los Alamos Center for Quantum Science and the center's head of the center's algorithm and simulation thrust. The center is a multi-institutional collaboration led by Oak Ridge National Laboratory.

Barren plateaus are regions in the mathematical space of optimization algorithms where problem-solving power increases exponentially as the size of the system under study increases. The phenomenon, described in a recent paper by a related group at Rouse Alamos, severely limits the trainability of large-scale quantum neural networks.

"Recent work has identified the potential of quantum machine learning as a powerful tool in our understanding of complex systems," said study co-author Andreas Albrecht. Albrecht is a professor at the University of California, Davis. Director of the Center for Quantum Mathematics and Physics and Distinguished Professor in the Department of Physics and Astronomy. "Our work points to fundamental considerations that limit the capabilities of this tool. "

In the Hayden Preskill thought experiment, Alice tries to break the secret encoded in a quantum state by putting it into nature's fastest scrambler (a black hole). Bob and Alice are fictional quantum dynamics duos often used by physicists to represent subjects in thought experiments.

"You might think this would make Alice's secret fairly safe, but Haydn and Preskill argue that if Bob knew the overall dynamics achieved by the black hole and shared the maximum entangled state with the black hole," Holmes said. , it is possible to decode Alice's secret by collecting some other photons emitted from the black hole. But this raises the question, how does Bob learn the dynamics implemented by the black hole? Well, not by using quantum machines, according to our findings study."

A key part of the new theorem developed by Holmes and her co-authors assumes no prior knowledge of quantum scramblers, a situation unlikely to occur in real-world science.

"Our work draws attention to the enormous leverage that even small amounts of prior information may play in our ability to extract information from complex systems and potentially reduce the power of our theorems," Albrecht said. Processing power can vary widely in different situations (from our scan from the theory of black holes to the specific situations human-controlled on Earth), where our theorems are still fully valid, and where the theorems can be evaded in some cases case, future research may come up with some interesting examples.