Researchers at the University at Buffalo have enhanced a computationally efficient technique referred to as the truncated Wigner approximation (TWA), a type of physics shortcut that simplifies quantum mathematics, to tackle issues previously believed to require extensive computing resources. The study was published in PRX Quantum.
Envision delving into matter at the quantum level, where minuscule particles can engage in over a trillion configurations simultaneously.
This is no easy feat. Physicists often rely on supercomputers or artificial intelligence to model quantum systems and explore their possible states.
The physics community has recognized this possibility for years, yet turning it into reality has proven to be more intricate.
The study offers a practical and accessible TWA template that enables physicists to input their specific problems and obtain usable results within a matter of hours.
Our approach offers a significantly lower computational cost and a much simpler formulation of the dynamical equations. We think this method could, in the near future, become the primary tool for exploring these kinds of quantum dynamics on consumer-grade computers.
Jamir Marino, Assistant Professor and Study Corresponding Author, College of Arts and Sciences, University of Buffalo
Marino, who joined UB this fall, conducted the research while at Johannes Gutenberg University Mainz in Germany. Two of his former students from Mainz, Hossein Hosseinabadi and Oksana Chelpanova, are co-authors on the study. Chelpanova is now a postdoctoral researcher in Marino’s lab at UB.
The research received funding from the National Science Foundation, the German Research Foundation, and the European Union.
Taking a Semiclassical Approach
Not every quantum system can be solved with complete precision. Achieving this would be impractical, as the necessary computational power increases exponentially with the complexity of the system.
Instead, physicists frequently utilize what is referred to as semiclassical physics, a balanced approach that retains sufficient quantum characteristics for accuracy while omitting details that have minimal impact on the results.
The Truncated Wigner Approximation (TWA) is one such semiclassical method that originated in the 1970s, but it is confined to isolated, idealized quantum systems where there is no gain or loss of energy.
Consequently, Marino’s team has adapted TWA for the more complicated systems encountered in the real world, where particles are continuously influenced by external forces and dissipate energy into their environment, a phenomenon known as dissipative spin dynamics.
Plenty of groups have tried to do this before us. It’s known that certain complicated quantum systems could be solved efficiently with a semiclassical approach. However, the real challenge has been to make it accessible and easy to do.
Jamir Marino, Assistant Professor and Study Corresponding Author, College of Arts and Sciences, University of Buffalo
Making Quantum Dynamics Easy
The researchers attempting to utilize TWA encountered significant complexity. The team applied the method to a new quantum issue; they were required to re-derive the mathematics from the beginning.
As a result, Marino’s team turned what was once a long series of complex, often inaccessible mathematical expressions into a straightforward conversion table, making it much easier to translate quantum problems into manageable equations.
“Physicists can essentially learn this method in one day, and by about the third day, they are running some of the most complex problems we present in the study,” said Chelpanova.
Saving Supercomputers for the Big Problems
The expectation is that the innovative method will preserve supercomputing clusters and AI models for the genuinely complex quantum systems. These systems cannot be addressed using a semiclassical approach. They encompass not merely a trillion potential states, but an amount of states that exceeds the number of atoms in the universe.
“A lot of what appears complicated isn’t actually complicated. Physicists can use supercomputing resources on the systems that need a full-fledged quantum approach and solve the rest quickly with our approach,” said Marino.
Journal Reference:
Hosseinabadi, H., et al. (2025) User-Friendly Truncated Wigner Approximation for Dissipative Spin Dynamics. PRX Quantum. doi.org/10.1103/1wwv-k7hg