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Researchers have used a quantum algorithm for the first time to solve a complex mathematical problem that for over a century was considered insurmountable even for the most powerful supercomputers. The problem involves the factorization of group representations, a fundamental operation used in particle physics, materials science, and data communications.
The work was led by Los Alamos National Laboratory scientists Martin Larocca and IBM researcher Vojtech Havlicek. The results were published in the journal Physical Review Letters.
Scientists recall that Peter Shor demonstrated the possibility of factoring integers on a quantum computer. Now, it has been shown that similar methods are applicable to symmetries. Essentially, we are talking about breaking complex structures into their “indecomposable representations,” the fundamental building blocks.
For classical computers, this task becomes prohibitive when dealing with complex systems. Identifying these blocks and calculating their number (so-called “multiplicative numbers”) requires enormous computational resources.
The new algorithm is based on the quantum Fourier transform, a family of quantum circuits that allows the efficient implementation of transformations used in classical mathematics to analyze signals. More details are provided in a press release from Los Alamos National Laboratory.
Scientists emphasize that this is a demonstration of “quantum advantage,” which is when a computer Quantum computing can handle a task that traditional machines cannot. They believe it is examples like this that determine the practical value of quantum technologies.
The article emphasizes that researchers have succeeded in identifying a class of problems in representation theory that enable efficient quantum algorithms. At the same time, they describe a parametric regime in which a real increase in productivity is possible.
The practical significance of the work is broad. In particle physics, the method can be used to calibrate detectors. In data science, it can be used to create reliable error-correcting codes for storing and transmitting information. In materials science, it helps to better understand the properties of substances and design new materials.
Therefore,Larocca and Havlicek’s work expands the range of problems where quantum computing truly opens new horizons. As the authors emphasize, the main challenge for science today is simple: it is necessary to determine precisely how quantum computers can bring real benefits and demonstrate advantages over classical systems.
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