A new theorem from the field of quantum machine learning has left a major hole in the accepted understanding of information scrambling.
“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 learning of process unknown, “said Zoe Holmes, post-doc at Los Alamos National Laboratory and co-author of the article describing the work published today in Physical examination letters.
“Fortunately, because most physically interesting processes are simple or structured enough that they don’t look like a random process, the results don’t condemn quantum machine learning, but rather underscore the importance of understanding its limits,” said Holmes. .
In Hayden-Preskill’s classic thought experiment, a fictional Alice throws information such as a book into a black hole that scrambles the text. His companion, Bob, can still retrieve him using entanglement, a unique feature of quantum physics. However, the new work proves that the fundamental constraints on Bob’s ability to learn the details of the physics of a given black hole mean that reconstructing the information in the book is going to be very difficult, if not impossible.
“Any information transmitted by an information scrambler such as a black hole will reach a point where the machine learning algorithm gets stuck on a sterile plateau and therefore becomes impossible to learn. This means that the algorithm cannot learn. jamming processes, “said Andrew Sornborger, a computer. scientist in Los Alamos and co-author of the article. Sornborger is director of the Quantum Science Center in Los Alamos and the centre’s algorithm and simulation leader. The Center is a multi-institutional collaboration led by Oak Ridge National Laboratory.
Bare plateaus are regions of the mathematical space of optimization algorithms where the ability to solve the problem becomes exponentially more difficult as the size of the system studied increases. This phenomenon, which considerably limits the training of large-scale quantum neural networks, was described in a recent article by a related team at Los Alamos.
“Recent work has identified the potential of quantum machine learning as a formidable tool in our attempts to understand complex systems,” said Andreas Albrecht, co-author of the research. Albrecht is Director of the Center for Mathematics and Quantum Physics (QMAP) and Professor Emeritus, Department of Physics and Astronomy, at UC Davis. “Our work highlights fundamental considerations that limit the capabilities of this tool.”
In the Hayden-Preskill thought experiment, Alice attempts to destroy a secret, encoded in a quantum state, by throwing it into nature’s fastest jammer, a black hole. Bob and Alice are the fictional quantum dynamic duo typically used by physicists to represent agents in a thought experiment.
“You might think that would make Alice’s secret pretty safe,” said Holmes, “but Hayden and Preskill argued that if Bob knows the unitary dynamics implemented by the black hole and shares a maximally entangled state with the hole black it is possible to decode Alice’s secret by collecting a few extra photons emitted by the black hole. But that begs the question, how could Bob learn the dynamics implemented by the black hole? Well, not by using the black hole. ‘quantum machine learning, according to our results. “
A key part of the new theorem developed by Holmes and his co-authors assumes no prior knowledge of the quantum jammer, a situation unlikely to occur in real-world science.
“Our work draws attention to the enormous leverage that even small amounts of prior information can play in our ability to extract information from complex systems and potentially reduce the power of our theorem,” said Albrecht. “Our ability to do this can vary widely in different situations (as we move from the theoretical examination of black holes to concrete situations controlled by humans here on earth). Future research is likely to provide interesting examples, in two situations where our theorem remains fully in force, and others where it can be evaded.