Newswise – Neural networks revolutionized the machine learning of classical computers: self-driving cars, language translation, and even artificial intelligence software are all possible. It's no wonder researchers wanted to transfer this same power to a quantum computer, but every attempt to do so has led to unexpected problems. However, recently, the team at Los Alamos National Laboratory has developed a new way of bringing these same mathematical concepts to quantum computers by leveraging what is called the Gaussian process.
“The goal of this project was to see if we could prove that a genuine quantum Gaussian process exists,” said Marco Cerezo, lead scientist for the Los Alamos team. “Results like this will spur innovations and new forms of morphology that implement quantum machine learning.”
One of the most fundamental breakthroughs in the field of machine learning came after the realization that large neural networks converged into Gaussian processes. A neural network can contain millions of “neurons.” This is an essentially mathematical node that makes educated guesses about a particular information. Although not individually random and unfair, after millions of guesses, the information processed by these neurons fits a Gaussian curve, also known as the Bell curve, allowing researchers to extrapolate the mean.
Essentially, the team was able to prove that the same Gaussian curve applies to several quantum computing processes. This is a development that promises to significantly alter quantum computing capabilities.
The Los Alamos team outlines the findings from a new paper published in Journal Nature Physics.
New learning methods avoid known issues
Neural networks are one family known as “parametric models” and work by leveraging variational parameters that can be adjusted to “learn” yourself. After success with classical computing, scientists wanted to leverage neural networks for quantum computing. This has made it more powerful for these machines and promised to perform tasks that are too complicated for classic computers.
However, after years of research, the lab team discovered that parametric models of quantum computing settings tend to cause unexpected problems such as barren plateaus that lead to mathematical dead ends.
“The problem with quantum neural networks was that we were copying and pasting classic neural networks and pasting them onto quantum computers,” says Martin Larocca, a lab scientist who specializes in quantum algorithms and quantum machine learning. “This doesn't seem to work as easily as I expected. So I wanted to go back to the basics and find a simpler, more restrictive way of learning, but it actually works and has certain guarantees too.”
Unlike neural networks, Gaussian processes are not parametric, and thus avoid many of the problems mentioned above. However, Gaussian's process is not a general purpose tool. If the distribution does not follow the Bell curve, the resulting prediction is inaccurate. So the team used advanced mathematics tools that can check mathematics and confirmed that the new method is Gaussian and is a suitable and accurate means of processing quantum data sets on quantum computers.
“This is the holy grail of Bayesian learning,” said Diego Garcia Martin, the first author of the paper. “More than mathematical curiosity, our results have concrete practical meaning. We say we need to predict the home price. We start with the first guess that prices follow a simple bell curve. So, like a house or its price, we can use this Gaussian process to update the bell curve, and find new ones for home prices. Gaussian process regression.
New Quest
Replication of the power of neural networks in quantum computers has been a long-standing goal in this field. This paper records years of work for a team and is the first time this feature has been proven in mathematics.
As quantum computers are still an early technology, this work and much of the research conducted in the field of quantum machine learning models are still theoretical. This is necessary to ensure that if a powerful quantum computer is ultimately developed, researchers have equally powerful machine learning models to solve the world's most complex and otherwise cumbersome problems.
As part of a larger work, the paper points to new directions that teams want to pursue the quantum community. Essentially, researchers should stop forcing models designed for classical computing to fit into the realm of quantum machine learning.
“This is a quest we had,” Celeso said. “We need to find new ways to do quantum machine learning, rather than keeping dead horses down by recycling old methods.”
paper: “Quantum neural networks form Gaussian processes” Natural physics.
doi:10.1038/s41567-025-02883
Funds: Institute-supervised research and development program, the nonlinear research center at Los Alamos National Laboratory, and the ASC Beyond Moore legal project at Los Alamos National Laboratory.
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