{"id":158043,"date":"2025-09-21T04:11:17","date_gmt":"2025-09-21T04:11:17","guid":{"rendered":"https:\/\/www.newsbeep.com\/au\/158043\/"},"modified":"2025-09-21T04:11:17","modified_gmt":"2025-09-21T04:11:17","slug":"quantum-computers-tackle-century-old-math-puzzle","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/au\/158043\/","title":{"rendered":"Quantum Computers Tackle Century-Old Math Puzzle"},"content":{"rendered":"

\"\"<\/a>A Los Alamos scientist has shown that quantum computers can be used to \u2018factorize\u2019 group representations, a mathematical concept used in particle physics, engineering and many other fields. Image created in GPT-4o<\/p>\n

LANL News:<\/p>\n

A Los Alamos scientist has shown that quantum algorithms can be used to factor group representations \u2014 a problem central to particle physics and many other fields \u2014 that was thought to be infeasible for computers at any practical scale<\/p>\n

Los Alamos National Laboratory researcher Mart\u00edn\u202fLarocca and Vojt\u011bch Havl\u00ed\u010dek, a researcher at IBM, have shown that quantum computers can crack a family of complex problems involving group representations, which are sets of matrices that embody an abstract group, and that have stumped today\u2019s greatest supercomputers. This discovery offers more evidence of quantum advantage, and it buoys the need for the nation to establish itself as a global leader in quantum computing.<\/p>\n

\u201cThe challenge for quantum computing at this moment is straightforward,\u201d said Larocca, a scientist and the paper\u2019s first author. \u201cWe 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.\u201d<\/p>\n

In a paper published by Physical\u202fReview\u202fLetters<\/a>, Larocca and Havl\u00ed\u010dek show that quantum computers can be used to \u201cfactorize\u201d group representations into their indivisible building blocks, called irreducible representations. These problems are used widely in scientific fields ranging from engineering to particle physics and beyond.<\/p>\n

In a larger sense, insights like those found in this paper are guiding researchers\u2019 current understanding of what quantum computers are capable of.<\/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

Solving the unsolvable<\/p>\n

The field of quantum computing is in a race on two fronts: the first, to develop the hardware that can make large-scale quantum computers a reality; the second, to explore the quantum advantage \u2014 problems for which quantum computing is faster, more efficient, or more accurate than classical computing. It is in this latter category that Larocca\u2019s paper offers valuable insights.<\/p>\n

Whenever scientists describe the different ways something can be rearranged \u2014 atoms in a crystal, qubits in a circuit, pixels in an image \u2014 they often reach for the group representation, the set of all possible swaps of an item. A group representation turns those abstract swaps into concrete matrices that computers can then manipulate. For example, every time physicists describe how a particle can spin, vibrate or trade places with its neighbors, they use group representations.<\/p>\n

Just as any whole number can be broken into its prime factors (the number 12, for example, can be equally divided by 1, 2, 3, 4 and 6), any group representation is capable of being broken into its core building blocks, called \u201cirreducible representations.\u201d But even the fastest classical supercomputers are stumped when it comes to solving these problems \u2014 especially when it comes to multiplicity numbers, which count how many times each building block appears in the problem.<\/p>\n

The 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. With this, Larocca and Havl\u00ed\u010dek were able to factor several common group representations.\u00a0<\/p>\n

When scientists calibrate particle\u2011physics detectors, they rely on factoring group representations to find these multiplicity numbers. Error-correcting codes, used in data transmission and storage, also rely on this technique. The method is also critical in advanced material design.<\/p>\n

\u201cComputer scientist Peter Shor showed that quantum computers can factor integers,\u201d Larocca said. \u201cHere, we\u2019re showing they also allow us to factor symmetries.\u201d<\/p>\n

About the research<\/p>\n

The research was published in the journal Physical Review Letters.
\nPaper: \u201cQuantum Algorithms for Representation-Theoretic Multiplicities.\u201d Physical Review Letters.
\nDOI:\u00a0doi.org\/10.1103\/k5tx-xtr3<\/a>
\nFunding: This work was funded by the Center for Nonlinear Studies at Los Alamos National Laboratory and by the Laboratory Directed Research and Development (LDRD) program.<\/p>\n","protected":false},"excerpt":{"rendered":"A Los Alamos scientist has shown that quantum computers can be used to \u2018factorize\u2019 group representations, a mathematical…\n","protected":false},"author":2,"featured_media":158044,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21],"tags":[64,63,257,105],"class_list":{"0":"post-158043","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-computing","8":"tag-au","9":"tag-australia","10":"tag-computing","11":"tag-technology"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts\/158043","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/comments?post=158043"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts\/158043\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/media\/158044"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/media?parent=158043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/categories?post=158043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/tags?post=158043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}