Researchers at Los Alamos National Laboratory have described a new theorem of quantum machine learning based on the Hayden-Preskill thought experiment. The theorem, which calls into question the way that physicists have previously understood information scrambling in random processes, is published in Physical Review Letters.
The Hayden-Preskill thought experiment theorizes a scenario where Alice and Bob are the fictitious quantum pair. The experiment considers what happens when Alice throws a book into a black hole that scrambles the text. (Black holes are an example of random processes.) Bob attempts to bring back the book by using entanglement (see the video above) but is limited by what is known in quantum physics as a barren plateau. As explained by Science Daily, a barren plateau is an area in the mathematical space of optimization algorithms where the ability to solve the problem becomes exponentially harder as the size of the system being studied increases. Thus, at a certain point, Bob will not be able to retrieve the book.
"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 co-author Zoe Holmes.
"Any information run through an information scrambler such as a black hole will reach a point where the machine learning algorithm stalls out on a barren plateau and thus becomes untrainable. That means the algorithm can't learn scrambling processes," adds study co-author Andrew Sornborger who is the Director of Quantum Science Center at Los Alamos and leader of the Center's algorithms and simulation thrust.
"Recent work has identified the potential for quantum machine learning to be a formidable tool in our attempts to understand complex systems," notes coauthor Andreas Albrecht, who is Director of the Center for Quantum Mathematics and Physics (QMAP) and Distinguished Professor of the Department of Physics and Astronomy at UC Davis. "Our work points out fundamental considerations that limit the capabilities of this tool."
"Thankfully, because most physically interesting processes are sufficiently simple or structured so that they do not resemble a random process, the results don't condemn quantum machine learning, but rather highlight the importance of understanding its limits," Holmes concluded.