They reduce the problem of quantum physics from a thousand equations to four. Why is it so important?

The artificial intelligence algorithm, developed by an international team of scientists from 8 universities and research centers around the world, has reduced the number of equations used in a quantum physics problem from 100,000 to just four, and without loss of accuracy. This result is a significant step forward in the study of many-body systems, such as systems with many electrons, and was recently published in the journal Physical Review Letters.

With this work, they were able to capture the motion of electrons moving through a square lattice in simulations that so far have required hundreds of thousands of individual equations. If this method can be adapted to other situations, it could help create materials with desired characteristics, such as being superconductive or useful for producing clean energy.

The computational feat is a revolution in understanding and describing the crazy world of the little ones. As explained at the Flatiron Institute, this would help solve one of the most difficult problems in quantum physics, the “n” body problem, which attempts to describe systems containing, for example, a large number of electrons interacting with each other. .

But what does it mean? Why is what has been achieved so relevant? Let’s start from the beginning:

The 20th century brought with it new physics

Quantum physics in the field of physics that studies the smallest things, how they work, how they interact, etc. It arose at the end of the 19th century with the hands of Max Planck.

Planck showed that the physics that existed up to that time was insufficient to explain the radiation of energy by a hot object. It turned out that everything coincides when the energy emitted by the body exceeds a certain constant by an integer number of times, which also has no classical comparison. Planck was suspicious of his discovery until the evidence became clear, as the experimental data of other scientists are in perfect agreement with his theory.

The two giant steps towards accepting Planck’s theory were taken in that order by Albert Einstein and Niels Bohr.

Einstein used quantum theory to demonstrate the photoelectric effect described decades earlier by Heinrich Hertz.

On the other hand, Niels Bohr proposed a model of the atom in which electrons could only occupy orbits whose angular momentum would be an integer multiplied by the reduced Planck’s constant. Both were awarded the Nobel Prize in Physics in 1905 and 1922, respectively.

Complex problems that are difficult to solve

Solving exactly physical problems involving more than two bodies is not an easy task. A classic example of this is the famous three-body problem, which is to find, at any given time, the trajectories of three bodies with mass subject to gravitational attraction, given their initial conditions of position and velocity. The problem that a priori may seem simple because they only three bodies and the gravitational interaction are well known, it is not so. In fact, this is a chaotic system, that is, with a very small change in the initial conditions, the system develops in a completely different way.

We can assume that if the three-body problem does not have an analytical solution, the more so the problem involving a larger number of bodies, say, No. It’s called a problem No body.

Most of the work done in this direction is devoted to gravitational interaction, but other problems of a different nature can also be attributed to the problems of gravitational interaction. No body. For example, modeling large molecules, such as proteins, or the dynamics and interactions of groups of elementary particles, such as electrons.

Renormalization group

Analysis of the dynamics of a group of electrons under given initial conditions is an extremely complex problem, the numerical solution of which is not easy to obtain. This problem involves several quantities such as spin, charge, etc. One way to solve this problem is to use the call renormalization group.

There are two options. The first is to capture blocks of multiple particles and treat them as one “fat” particle. This process can be repeated several times, reducing the dimension of the problem. The second option is to reduce the spatial resolution of the problem, sacrificing it for the sake of obtaining an acceptable result.

In any case, there are problems in physics in which it is difficult to find a numerical solution even with the help of a renormalization group, since the number of equations used is huge, and the computational power required to solve them is unaffordable. Perhaps with quantum computing this would be feasible, but at the moment it is not possible.

Artificial intelligence to the rescue

And here we come to the need to reduce the problem of quantum physics from a thousand equations to four.

Recently, a team of researchers from Europe and the US used an artificial intelligence algorithm to reduce the number of equations involved in the quantum analysis of the two-dimensional Hubard model from 100,000 to just four, all without losing accuracy.

The Hubard model is the simplest physical model describing the interaction between network particles, understood as a quasi-regular distribution of particles in one, two or three dimensions, with only two terms in the Hamiltonian (energy), one related to the kinetic one. with speed and other potential associated with the proximity of other particles.

In the case of the two-dimensional Hubard model, the number of variables seems to be enormous, since it is necessary to take into account the connections between each pair of particles.

On the contrary, as the authors of the publication demonstrate, the dimension of the problem can be reduced without loss of accuracy using artificial intelligence algorithms and machine learning. To do this, they used a neural network called Neural Ordinary Differential Equations.

Details of the process they carried out can be found in the original publication, but let’s focus on artificial intelligence and machine learning They are likely to be key players in many upcoming scientific and technological discoveries, so we better be prepared.

Francisco José Torcal Milla, professor. Department of Applied Physics. Center: EINA. Institute: I3A, University of Zaragoza

This article was originally published on The Conversation. Read the original.

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