Scientists have reduced the complexity of a challenging quantum issue that
formerly required 100,000 equations to as few as four equations using
artificial intelligence, all without compromising accuracy. The research,
which was released in the Physical Review Letters on September 23, has the
potential to completely alter how scientists study systems with lots of
interacting electrons. Furthermore, the technique may help in the creation
of materials with desired features like superconductivity or usefulness for
the production of renewable energy if it is scalable to other issues.
"We utilize machine learning to reduce this massive object of
interconnected differential equations to a size that is small enough to be
counted on your fingers," explains Domenico Di Sante, the lead author of the
study. Di Sante is an assistant professor at the University of Bologna in
Italy and a visiting research fellow at the Center for Computational Quantum
Physics (CCQ) at the Flatiron Institute in New York City.
The difficult issue is how electrons behave when they go through a lattice
that resembles a grid. Two electrons interact when they are located at the
same lattice location. This configuration, referred to as the Hubbard model,
idealizes a number of significant material classes and helps scientists
understand how electron behavior leads to desired phases of matter, such
superconductivity, in which electrons pass through a material without
encountering resistance. Additionally, the model is used to test new
techniques before releasing them onto more intricate quantum systems.
Still, the Hubbard model is very straightforward. However, the issue takes
significant computer power, even for moderate numbers of electrons and
state-of-the-art computational methods. This is due to the possibility of
quantum mechanical entanglement between electrons when they interact:
Physicists have to deal with all the electrons at once instead of treating
each one separately since the two electrons cannot be dealt separately even
though they are separated by a great distance on separate lattice sites. As
the number of electrons increases, more entanglements arise, increasing the
computational difficulty dramatically.
Using a renormalization group is one method of analyzing a quantum system.
Scientists may examine how a system's behavior, like the Hubbard model,
changes as they alter its attributes, like its temperature, or examine it at
different scales using this mathematical tool. Unfortunately, there can be
tens of thousands, hundreds of thousands, or even millions of unique
equations in a renormalization group that maintains track of all conceivable
couplings between electrons while sacrificing as little as feasible.
Furthermore, the equations are challenging: Each one depicts the interaction
of two electron pairs.
Dinte and his associates pondered if they might utilize a neural network—a
machine learning instrument—to help manage the renormalization group. The
neural network can be compared to a hybrid of the scrambling switchboard
operator and evolution's survival-of-the-fittest theory. First, inside the
full-size renormalization group, the machine learning algorithm establishes
connections. Afterwards, the neural network adjusts the connections'
strengths until it discovers a tiny set of equations that produce the same
answer as the initial, jumbo-size renormalization group. With just four
equations, the program's output accurately represented the physics of the
Hubbard model.
According to Di Sante, "it's basically a machine that has the ability to
find hidden patterns." We exclaimed, 'Wow, this is more than we imagined,'
as soon as we saw the outcome.'" We truly succeeded in capturing the
pertinent physics."
It took weeks for the machine learning algorithm to run, and a lot of
processing power was needed for training. The good news, according to Di
Sante, is that they can modify their program to focus on different
difficulties without having to start from scratch now that they have a coach
for it. Additionally, he and his colleagues are looking into what the
machine learning is really "learning" about the system, which might provide
physicists additional insights that they might not otherwise be able to
understand.
The main unanswered question is ultimately how well the new method performs
on more intricate quantum systems, including materials where electrons
interact across large distances. Furthermore, Di Sante notes that there are
intriguing prospects for using the method in other domains that deal with
renormalization groups, such cosmology and neurology.
