Researchers have successfully used a quantum algorithm to solve a complex century-old mathematical problem long considered impossible for even the most powerful conventional supercomputers.<\/p>\n
The achievement has direct applications in fields including particle physics, material science, and data transmission.<\/p>\n
\u201cIs there a computational problem that has an efficient quantum algorithm but no efficient randomized algorithm? Quantum computing is driven by the belief that the answer is yes,\u201d said the researchers in a new study.<\/p>\n
Factoring group representations<\/p>\n
The work was conducted by Mart\u00edn Larocca, a scientist at Los Alamos National Laboratory, and Vojt\u011bch Havl\u00ed\u010dek, a researcher at IBM.\u00a0<\/p>\n
In a paper published in Physical Review Letters, they demonstrate that quantum computers can \u201cfactor group representations,\u201d a foundational task<\/a> in several scientific disciplines.<\/p>\n \u201cComputer scientist Peter Shor showed that quantum computers can factor integers,\u201d Larocca explained, referencing a famous discovery in the field. \u201cHere, we\u2019re showing they also allow us to factor symmetries.\u201d<\/p>\n The problem is conceptually similar to finding the prime factors of a number, like breaking down 12 into 2, 2, and 3. Scientists use group representations to describe all the possible arrangements or transformations of a system, such as atoms in a crystal.<\/p>\n These representations can be broken down into their fundamental building blocks, known as \u201cirreducible representations.\u201d<\/p>\n For classical computers, finding these blocks and counting them (\u201cmultiplicity numbers\u201d) becomes an exceedingly difficult task for complex systems<\/a>.<\/p>\n Example of quantum advantage<\/p>\n The new research shows that an algorithm using quantum Fourier transforms can perform this factorization efficiently.<\/p>\n \u201cThe new paper uses quantum Fourier transforms, a family of quantum circuits that compile certain group-theoretic transforms, including the well-known discrete Fourier transform, which decomposes discrete time signals into its frequency components,\u201d highlighted the researchers in a press release<\/a>.<\/p>\n This success is a clear example of \u201cquantum advantage,\u201d where quantum computers can solve meaningful problems that are intractable for classical machines.<\/p>\n \u201cThis is the essence of quantum computing research,\u201d Larocca said. \u201cWe want to find quantum algorithms that display speedups over classical algorithms.\u201d<\/p>\n