In a notable stride toward advancing quantum computing, mathematicians at Utah State University (USU) have developed topological theories with the potential to overcome some of the technology's major hurdles. USU mathematicians Nathan Geer and Matthew Young, along with a global network of collaborators, have delved into non-semisimple topological quantum field theories (TQFTs) that they began formulating about 14 years ago, a study that was initially driven by pure mathematical interest.
According to a statement by Geer, a professor at USU's Department of Mathematics and Statistics, their abstract work on TQFTs is now "directly relevant to quantum physics." Their findings indicate that non-semisimple theories are more potent than the traditional semisimple ones, and they boast unique properties that can predict the existence of new quantum particles. Geer conveyed to USU Today the potential of these properties to facilitate breakthroughs in quantum computing implementations.
Quantum computing, while promising exponentially greater computational power, grapples with the fragility of quantum bits, or "qubits," which can represent 'yes' and 'no' simultaneously, unlike the binary bits of classical computers. Young points out a significant quantum computing challenge: maintaining the precise control of quantum systems. "A challenge with this technology is preventing errors from entering the system, causing particles to, using the building block analogy, shift and topple out of place," Young told USU Today.
The TQFT research by Geer, Young, and their team may enhance stability for qubits, spreading information out over a more robust area. This approach is detailed in a recent paper by Aaron Lauda, Professor and Dean at the University of Southern California and a collaborator of Geer and Young, proposing new qubits termed "neglectons," noted in PhysicsWorld and Scientific American articles. "The name neglecton was chosen because these quasi-particles are neglected in more traditional semisimple approaches," Geer said via USU Today, outlined in a publication featured in Nature Communications.
Both Geer and Young, recipients of the National Science Foundation CAREER research award, continue to explore non-semisimple TQFT and its possible implications for the future of quantum computing. Geer reflects on the pursuit of theoretical math leading to tangible advances, expressing that it would be a "dream come true" to witness a real-world discovery stemming from their mathematical groundwork, as reported by USU Today.
