In the end, it is about a very small change: a couple of lines in a code that contains approximately 10,000 lines. And yet suddenly an artificial neural network can be trained a lot quicker, opening up completely new possibilities in the context of so-called neural quantum states. This very effective optimisation method was developed by Ao Chen, a doctoral candidate from the working group Theoretical Physics III: Correlated Quantum Materials at the Institute of Physics at the University of Augsburg.

Simple optimisation with great effect

“The reformulation developed by Chen slightly modifies a numerical method known as stochastic reconfiguration. Chen’s reformulation is so simple that one is inclined to ask why no one had previously thought of it; yet it is a new idea with immense potential,” says Markus Heyl, professor for theoretical physics III, who is supervising Chen’s doctoral thesis. The results have been published in an article in the renowned journal Nature Physics. 

With Chen’s optimised method, calculations are now much quicker while maintaining the same degree of accuracy, which is of great importance for a quantitative science like physics. As a consequence, much larger artificial neural networks can be trained than previously. That means networks with approximately one million artificial neurons can be trained, which is a factor of 100 more powerful than what was up until now feasible within the context of neuronal quantum states. This means that complex quantum mechanical problems that were previously inaccessible can now be solved for the first time.

Little researched state of matter

In general, the calculation of quantum mechanical systems of many particles is extremely complicated, even on the world’s largest supercomputers. In particular, this effects so-called frustrated quantum magnetic systems that can realise a special state of matter at very low temperatures: namely, quantum spin liquids (QSL). In contrast to almost all other typical quantum magnets, and contrary to all expectations, no actual magnet is formed, but rather a highly quantum-mechanically entangled state. This entanglement makes QSL very robust, which is one of many properties that make QSL suitable for applications in quantum information.

Due to the fact that QSL are so difficult to describe theoretically, up until now there has been a lack of modelling in many relevant systems that would enable experimental verification. For example, up until now it was unclear whether QSLs in so-called frustrated Heisenberg magnets, an important subclass of quantum magnets, exhibit a so-called excitation gap. That is, it was unknown how much energy was needed to generate a fundamental excitation in a QSL.

New results with great potential

With the newly developed optimisation method, Chen has now been able to calculate this. His result: there is no excitation gap in the QSL of these frustrated Heisenberg magnets. This is an important first step towards more precisely understanding and calculating the properties of QSL and being able to verify them experimentally in future and at a later stage producing and utilising them in a targeted manner.

Heyl is certain that the new approach has great potential as it opens up many previously inaccessible classes of problems. “There are limits, but we don’t yet fully understand where they lie,” he admits. “The main question for us at the moment is to find out where this limit lies.” Over the coming months, both researchers would like to apply the approach to systems of interacting electrons, and then to other problems in two-dimensional quantum matter.

In addition to the publication, the two researchers are also making the artificial neural network optimised by Chen available in CERN’s Zenodo repository, a freely accessible database of current physics research data.

The article

Ao Chen and Markus Heyl: Empowering deep neural quantum states through efficient optimization
www.nature.com/articles/s41567-024-02566-1