Suppose someone – let’s call her Alice – has a book of secrets that she wants to destroy and throws it into a convenient black hole. Given that black holes are nature’s fastest scrambler and act like giant trash grinders, Alice’s secrets must be pretty safe, right?
Suppose your archenemy Bob has a quantum computer that is entangled with the black hole. (In entangled quantum systems, actions performed on a particle affect their entangled partners in a similar way, regardless of distance or even if some disappear into a black hole.)
A famous thought experiment by Patrick Hayden and John Preskill is that Bob can observe some particles of light emerging from the edges of a black hole. Then Bob can run these photons as qubits (the basic processing unit of quantum computing) through the gates of his quantum computer to reveal the particular physics that messed up Alice’s text. From this he can reconstruct the book.
But not so fast.
Our recent work on machine quantum learning suggests that Alice’s book may be gone forever.
QUANTUM COMPUTER FOR STUDYING QUANTUM MECHANICS
Alice may never have a chance to hide her secrets in a black hole. Still, our new no-go theorem about information scrambling has practical application to understanding random and chaotic systems in the rapidly growing areas of quantum machine learning, quantum thermodynamics, and quantum information science.
Richard Feynman, one of the great physicists of the 20th century, founded the field of quantum computing in a speech in 1981 when he proposed the development of quantum computers as a natural platform for simulating quantum systems. Otherwise they are notoriously difficult to study.
Our team at Los Alamos National Laboratory, along with other employees, has focused on the study of algorithms for quantum computers and, in particular, algorithms for machine learning – what some like to call artificial intelligence. The research sheds light on what types of algorithms will do real work on existing noisy mid-range quantum computers and on unresolved issues of quantum mechanics overall.
In particular, we have dealt with the training of variation quantum algorithms. They create a problem-solving landscape in which the peaks represent the high-energy (undesirable) points of the system or problem and the valleys are the low-energy (desired) values. To find the solution, the algorithm works its way through a mathematical landscape and examines its features one after the other. The answer lies in the deepest valley.
REALIZATION LEADS TO SMILING
We wondered if we could use quantum machine learning to understand scrambling. This quantum phenomenon occurs when entanglement grows in a system made up of many particles or atoms. Think of the initial conditions of this system as some kind of information – for example Alice’s book. When the entanglement between the particles within the quantum system increases, the information spreads widely; these crawl of information is key to understanding quantum chaos, quantum information science, random circuits, and a number of other topics.
A black hole is the ultimate scrambler. By studying it with a quantum variation algorithm on a theoretical quantum computer entangled with the black hole, we could investigate the scalability and applicability of machine quantum learning. We could also learn something new about quantum systems in general. Our idea was to use a quantum variation algorithm that takes advantage of the photons that have leaked through to learn about the dynamics of the black hole. The approach would be an optimization procedure – again, searching the mathematical landscape to find the lowest point.
If we found it, we would expose the dynamics inside the black hole. Bob could use this information to crack the scrambler’s code and reconstruct Alice’s book.
Now here is the ruble. The Hayden-Preskill thought experiment assumes that Bob can determine the dynamics of the black hole that encrypts the information. Instead, we found that the nature of scrambling prevents Bob from learning this dynamic.
EXPOSED ON A CABBAGE PLATEAU
The reason for this: The algorithm has stalled on a barren plateau, which is as grim in machine learning as it sounds. During machine learning, a barren plateau represents a problem-solving space that, as far as the algorithm can see, is completely flat. In this structureless landscape, the algorithm cannot find the downward slope; There is no clear path to the energy minimum. The algorithm just turns its wheels and can’t learn anything new. It does not succeed in finding the solution.
Our resulting no-go theorem states that any quantum machine learning strategy hits the dreaded barren plateau when applied to an unknown scrambling process.
The good news is that most physical processes aren’t as complex as black holes, and we often have prior knowledge of their dynamics, so the no-go theorem doesn’t condemn quantum mechanical learning. We just have to carefully choose the problems to which we apply it. And we probably won’t need machine quantum learning anytime soon to peer into a black hole to learn about Alice’s book – or something else.
So Alice can be sure that her secrets are safe after all.
This is an opinion and analysis article and the views expressed by the author or authors are not necessarily those of Scientific American.