Artificial Intelligence Solves Decades-Old Puzzle in Quantum Field Theory Simulations
A long-standing problem in particle physics has finally been resolved: how best to formulate quantum field theories on a lattice so they can be efficiently simulated on computers. The breakthrough, scientists say, has come from artificial intelligence (AI).
Why Quantum Field Theories Are So Hard to Simulate
Quantum field theories underpin modern physics, explaining how particles behave and interact. Yet many of the field's most challenging questions cannot be solved with traditional mathematics alone and instead vast and highly complex computer simulations.
The difficulty lies in the fact that quantum field theories can be implemented on computers in many different ways. While these approaches should, in theory, produce the same physical results, their practical performance varies dramatically.
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Searching for the Optimal Lattice Formulation
Some lattice formulations are too slow or inaccurate to be useful, while others prove remarkably efficient. For decades, researchers have searched for the optimal formulation.
Now, a collaboration led by TU Wien, alongside teams in the United states and Switzerland, has demonstrated that artificial intelligence can dramatically accelerate progress. The findings are published in Physical Review Letters.
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In the Computer, the Whole World Is a Grid
Breaking Reality Into Discrete Units
"If we want to study quantum field theories on a computer, we have to break them into discrete units—and that is nothing out of the ordinary," said David Müller from the Institute for Theoretical Physics at TU Wien.
He compared the process to:
- Digital images made up of individual pixels
- Spaceflight calculations relying on small, step-by-step time intervals
Building a Four-Dimensional Lattice
In particle physics, this approach involves constructing a four-dimensional lattice with three spatial dimensions and one time dimension. Each point on the lattice is stored in the computer, while the rules of quantum field theory determine how these points interact.
This makes it possible to simulate:
- High-energy particle collisions at CERN
- The behaviour of matter shortly after the Big Bang
Why Lattice Choices Matter
While space and time are continuous in quantum field theory, translating them onto a lattice introduces flexibility. Several different lattice formulations can represent the same continuous theory, but only some are computationally efficient.
Choosing the wrong formulation can cause simulations to stall or fail to reach accurate results within a practical timeframe.
Different Scale, Same Result
The Role of Fixed-Point Equations
A crucial factor behind this breakthrough lies in what physicists call fixed-point equations.
"Some lattice formulations of quantum field theory have a particularly elegant feature," explained Urs Wenger of the University of Bern. "They preserve certain physical properties even when the lattice is made coarser or finer."
Why Scale Independence Matters
When physical properties remain unchanged across different lattice resolutions, scientists can trust that the results reflect real physics rather than numerical artefacts.
The concept is similar to maps drawn at different scales: while many details change, core features such as national borders remain constant.
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The Success of Artificial Intelligence
As far back as three decades ago, scientists were already experimenting with ways to adapt lattice formulations. The problem was scale: the number of adjustable parameters ran into the hundreds of thousands—far beyond what any researcher could reasonably handle.
"Many people were exploring these ideas 30 years ago, but the necessary technology simply didn't exist," said Kieran Holland of the University of the Pacific. "By collaborating with colleagues at TU Wien, we were finally able to return to these long-standing concepts."
Custom-Built AI for Physics
To overcome this challenge, the team developed a highly specialized neural network designed specifically for quantum field theory. Off-the-shelf AI tools proved inadequate.
Instead, the researchers built an artificial intelligence system that strictly respects the underlying laws of physics.
A New Path for Quantum Simulations
That effort has now paid off. Using AI, the researchers successfully parameterized the action —the key physical quantity in quantum field theories, familiar from Planck's "quantum of action"—on a lattice in a way that delivers strikingly low errors, even on coarse grids.
"This work opens up an entirely new path for simulating complex quantum field theories with realistic computational resources," said Andreas Ipp of TU Wien.
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