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Imagine zooming into matter at the quantum scale, where tiny particles can interact in more than a trillion configurations at once.

If that sounds complicated, it is: Â鶹ÒùÔºicists often rely on supercomputers or even artificial intelligence to simulate such quantum systems and their possible states.

But what if many of these problems could instead be solved on an ordinary laptop?

The physics community has known this to be possible for years but making it a reality has been more complicated.

Now, physicists at the University at Buffalo have moved us much closer. They've extended a computationally affordable method known as the truncated Wigner approximation (TWA)—a sort of physics shortcut that makes quantum math more manageable—to problems once thought to require massive computing power.

Equally important, the approach, described in a study in September in PRX Quantum, also provides a practical, user-friendly TWA template that allows physicists to plug in their problem and get usable results in 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, Ph.D., 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, conducted work on the study while at Johannes Gutenberg University Mainz in Germany. The study's co-authors include two of his students there, Hossein Hosseinabadi and Oksana Chelpanova, the latter of whom is now a postdoctoral researcher in Marino's lab at UB.

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.

"Â鶹ÒùÔºicists 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.

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. "Â鶹ÒùÔºicists can use supercomputing resources on the systems that need a full-fledged quantum approach and solve the rest quickly with our approach."