While convolutional neural networks running on quantum computers have the potential to analyze quantum data better than classical computers can, a fundamental solvability problem - known as “barren plateaus” - has limited the application of these neural networks for large data sets. A "barren plateau" is a trainability problem that occurs in machine learning optimization algorithms when the problem-solving space turns flat as the algorithm is run.
“All hope of quantum speedup or advantage is lost if you have a barren plateau,” says physicist Marco Cerezo, coauthor of the paper on the research.
The crux of the problem is a “vanishing gradient” in the optimization landscape. The landscape is composed of "hills" and "valleys," and the goal is to train the model’s parameters to find the solution by exploring the geography of the landscape. The solution usually lies at the bottom of the lowest valley, but in a flat landscape one cannot train the parameters because it’s difficult to determine which direction to take.
That problem becomes particularly relevant when the number of data features increases. In fact, say the researchers, the landscape becomes exponentially flat with the feature size - hence, in the presence of a barren plateau, the quantum neural network cannot be scaled up.
However, using a novel graphical approach for analyzing the scaling within a quantum neural network and proving its trainability, the researchers were able to address this issue with a rigorous proof that guarantees scalability.
“The way you construct a quantum neural network can lead to a barren plateau - or not,” says Cerezo. “We proved the absence of barren plateaus for a special type of quantum neural network. Our work provides trainability guarantees for this architecture, meaning that one can generically train its parameters.”
As an artificial intelligence (AI) methodology, quantum convolutional neural networks are inspired by the visual cortex, say the researchers. As such, they involve a series of convolutional layers, or