New research is revealing how powerful quantum computers can be. For a long time, this technology has been only a concept rather than a reality. Two researchers made a significant quantum computing breakthrough. Their recent work shows that the machines can solve a class of problems that are too complex for the fastest supercomputers.
Los Alamos National Laboratory researcher Martín Larocca and Vojtěch Havlíček, a researcher at IBM, detailed their discovery in a paper in Physical Review Letters.
Quantum Outperforms the Fastest Supercomputers
Larocca and Havlíček’s paper focuses on “group representations.” These mathematical structures help scientists describe every way something can be rearranged, such as atoms in a crystal or pixels in an image. The core problem is breaking down the representations into basic building blocks, or factorization.
The researchers say it’s like trying to find the prime factors of a complex number. It’s a nearly impossible task for classical computers. According to the researchers, the real challenge is figuring out the “multiplicity numbers,” which count how many times the building blocks appear within a number.
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A powerful tool called the “quantum Fourier transform” found the solution.
Scientists applied it, and it successfully factored in several common group representations. They say it has real-world applications and is not just a theoretical exercise. For example, the researchers believe it could create new materials or even more effective error-correcting codes.
“The challenge for quantum computing at this moment is straightforward,” said Larocca. “We want to know what quantum computers are good at, so we looked at a set of problems that we know to be intractable to classical computers.”
This work is a significant step in the ongoing quest to prove that quantum computers can offer a true advantage over classical ones.
“Computer scientist Peter Shor showed that quantum computers can factor integers,” Larocca said. “Here, we’re showing they also allow us to factor symmetries.”
