Quantum Machine Learning Leaps Ahead: Overparametrization Unlocks Enhanced Performance

A revolutionary theoretical demonstration reveals that a method known as overparametrization improves performance in quantum machine learning for tasks that bewilder conventional computers.

"We anticipate our findings will be instrumental in harnessing machine learning to understand the characteristics of quantum data, like identifying various phases of matter in quantum materials research, a task extremely complex for classical computers," stated Diego Garcia-Martin, a postdoctoral researcher at Los Alamos National Laboratory. He is a contributing author of a new research paper by a Los Alamos team on this method in Nature Computational Science.

Study: Why bigger quantum neural networks do better. Image Credit: metamorworks / Shutterstock

Garcia-Martin undertook the research at the Laboratory's Quantum Computing Summer School in 2021 while a graduate student at the Autonomous University of Madrid.

Machine learning, or artificial intelligence, typically involves training neural networks to process information (data) and learn how to execute a specific task. Simplistically, one could envision the neural network as a box with knobs, or parameters, that accepts data as input and yields an output contingent on the knob settings.

"Throughout the training phase, the algorithm adjusts these parameters as it acquires knowledge, in pursuit of their optimal configuration," said Garcia-Martin. "Once the optimum parameters are identified, the neural network should be capable of extrapolating its learnings from the training examples to fresh and unencountered data points."

Both classical and quantum AI encounter a common hurdle while training the parameters, as the algorithm might settle for a sub-optimal setup during training and cease advancement.

Performance leap Overparametrization, a recognized principle in traditional machine learning that incrementally adds parameters, could circumvent this standstill.

The impacts of overparametrization on quantum machine learning models remained unclear until now. In the new paper, the Los Alamos team defines a theoretical structure to forecast the crucial count of parameters at which a quantum machine learning model becomes overparametrized. Upon reaching a particular tipping point, adding parameters triggers a performance boost, and the model becomes substantially easier to train.

"By devising the theory that underlies overparametrization in quantum neural networks, our study sets the stage for optimizing the training process and attaining superior performance in real-world quantum applications," elucidated Martin Larocca, the primary author of the paper and postdoctoral researcher at Los Alamos.

By leveraging elements of quantum mechanics such as entanglement and superposition, quantum machine learning promises far greater speed, or quantum advantage, compared to machine learning on classical computers.

Dodging obstacles in a machine learning landscape To portray the Los Alamos team's discoveries, Marco Cerezo, the senior scientist on the paper and a quantum theorist at the Lab, narrated a mental experiment in which a hiker in search of the highest mountain in a dim landscape symbolizes the training process. The hiker can move only in certain directions and assesses their progress by measuring altitude using a limited GPS system.

In this comparison, the number of parameters in the model corresponds to the paths available for the hiker to traverse, said Cerezo. "A single parameter permits movement to and fro, two parameters allow sideward movement and so on," he mentioned. A data landscape would likely consist of more than three dimensions, unlike our theoretical hiker's environment.

With too few parameters, the walker might fail to explore thoroughly and could mistake a minor hillock for the highest mountain or get stuck in a flat terrain where any step feels pointless. However, as the parameter count grows, the walker can maneuver in more directions in higher dimensions. What initially seemed like a local hill could, in fact, be a high valley between peaks. With these extra parameters, the hiker steers clear of getting stuck and identifies the real peak or the solution to the problem.