Picture diving deep into the quantum realm, where unimaginably small particles can exist and interact in more than a trillion possible ways at the same time.
It's as complex as it sounds. To understand these mind-bending systems and their countless configurations, physicists usually turn to powerful supercomputers or artificial intelligence for help.
But what if many of those same problems could be handled by a regular laptop?
Scientists have long believed this was theoretically possible, yet actually achieving it has proven far more difficult.
Researchers at the University at Buffalo have now taken a major step forward. They have expanded a cost-effective computational technique known as the truncated Wigner approximation (TWA), a kind of physics shortcut that simplifies quantum mathematics, so it can handle systems once thought to demand enormous computing power.
Just as significant, their approach -- outlined in a study published in September in PRX Quantum, a journal of the American Physical Society -- offers a practical, easy-to-use TWA framework that lets researchers input their data and obtain meaningful results within hours.
"Our approach offers a significantly lower computational cost and a much simpler formulation of the dynamical equations," says the study's corresponding author, Jamir Marino, PhD, assistant professor of physics in the UB College of Arts and Sciences. "We think this method could, in the near future, become the primary tool for exploring these kinds of quantum dynamics on consumer-grade computers."
Marino, who joined UB this fall, began this work while at Johannes Gutenberg University Mainz in Germany. His co-authors include two of his former students there, Hossein Hosseinabadi and Oksana Chelpanova, the latter now a postdoctoral researcher in Marino's lab at UB.
The research received support from the National Science Foundation, the German Research Foundation, and the European Union.
Taking a semiclassical approach
Not every quantum system can be solved exactly. Doing so would be impractical, as the required computing power grows exponentially as the system becomes more complex.
Instead, physicists often turn to what's known as semiclassical physics -- a middle-ground approach that keeps just enough quantum behavior to stay accurate, while discarding details that have little effect on the outcome.
TWA is one such semiclassical approach that dates back to the 1970s, but is limited to isolated, idealized quantum systems where no energy is gained or lost.
So Marino's team expanded TWA to the messier systems found in the real world, where particles are constantly pushed and pulled by outside forces and leak energy into their surroundings, otherwise 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," Marino says. "However, the real challenge has been to make it accessible and easy to do."
Making quantum dynamics easy
In the past, researchers looking to use TWA faced a wall of complexity. They had to re-derive the math from scratch each time they applied the method to a new quantum problem.
So, Marino's team turned what used to be pages of dense, nearly impenetrable math into a straightforward conversion table that translates a quantum problem into solvable 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," Chelpanova says.
Saving supercomputers for the big problems
The hope is that the new method will save supercomputing clusters and AI models for the truly complicated quantum systems. These are systems that can't be solved with a semiclassical approach. Systems with not just a trillion possible states, but more states than there are atoms in the universe.
"A lot of what appears complicated isn't actually complicated," Marino says. "Physicists can use supercomputing resources on the systems that need a full-fledged quantum approach and solve the rest quickly with our approach."
