Physicists have developed a way to model quantum systems on everyday computers, making it easier to run complex simulations without relying on supercomputers or artificial intelligence (AI) tools.
The new method updates "truncated Wigner approximation" (TWA), a decades-old technique for approximating quantum behavior, into a plug-and-play shortcut for solving complex calculations.
"Our approach offers a significantly lower computational cost and a much simpler formulation of the dynamical equations," study co-author Jamir Marino, an assistant professor of physics at the State University of New York at Buffalo, said in a statement. "We think this method could, in the near future, become the primary tool for exploring these kinds of quantum dynamics on consumer-grade computers."
A modern spin on a semiclassic
First developed in the 1970s, TWA is a "semiclassical" simulation method used to predict quantum behavior.
Quantum systems are governed by the rules of quantum mechanics and typically involve particles at impossibly small scales. At this level, phenomena like coherence and entanglement produce effects that can't be fully explained by classical physics alone.
Because these effects generate an enormous number of possible outcomes, simulating them often requires massive computing power — for example, supercomputer clusters or AI networks. To make quantum dynamics easier to study on conventional hardware, physicists often use a theoretical framework called semiclassical physics.
Semiclassical physics involves treating parts of a quantum equation through the lens of quantum mechanics and other parts with classical physics, allowing researchers to approximate how a quantum system might behave over time.
TWA works by transforming a quantum problem into multiple, simplified classical calculations, each starting with a small amount of statistical "noise" to account for the inherent uncertainty of quantum mechanics. By running these simplified calculations and averaging the results, researchers get a sufficient picture of how the quantum problem would play out.
However, TWA was initially developed for "idealized" quantum systems that are completely isolated from outside forces. This makes the math far more manageable because it assumes the system evolves without interference.
In reality, quantum systems are often open and exposed to external interference. Particles lose or absorb energy, or gradually lose coherence as they interact with their surroundings. These effects, known collectively as dissipative dynamics, fall outside the scope of conventional TWA and make it far more difficult to predict the behavior of quantum systems.
The researchers addressed this issue by extending TWA to handle Lindblad master equations — a widely used mathematical framework for modeling dissipation in "open" quantum systems. They then packaged the updated method into a "practical, user-friendly template" that serves as a conversion table, allowing physicists to plug in a problem and get usable equations within hours.
"Plenty of groups have tried to do this before us," Marino said. "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."
The updated technique also makes TWA reusable. Rather than having to rebuild underlying math from scratch for each new problem, physicists can enter their system's parameters into the updated framework and apply it directly. This lowers the barrier to entry and speeds up the math significantly, the team said.
"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," study co-author Oksana Chelpanova, a doctoral researcher at the University at Buffalo, said in the statement.
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