Mathematics for quantum computation and many-body theory (QOMBINE)

Kvantedatabehandling er en framvoksende teknologi med et stort potensiale til å løse viktige samfunnsmessige og teknologiske problemer. Imidlertid må store teoretiske og teknologiske hindringer overvinnes for å realisere kvantedatamaskiners fulle potensial, siden komponentene vekselvirker med hverandre og omgivelsene på utilsiktet vis. Dette begrenser nøyaktigheten og det fulle anvendelsesområde av kvantealgoritmer. Vi har som mål å utvikle nye matematiske metoder for å benchmarke, oppdage, undertrykke og korrigere feil i kvantedatamaskiner som følge av vekselvirkninger med omgivelsene. Dette vil bidra til å realisere kvantedatamaskiners potensielle fordeler. Videre vil vi utvikle et samlet matematisk rammeverk som kan anvendes på et bredt spekter av anvendelser innen kvantekjemi, et av de viktigste områdene for potensielt nyttige anvendelser av kvantedatamaskiner. Vi vil også studere ikke-klassiske trekk ved kvantemekanikk som muliggjør kvantekryptert kommunikasjon.

Modern computers and their ever improving computing power have defined the technological advancements of our times. Their performance will eventually reach its limits and a new computational paradigm is currently being developed to enable future advances: Quantum computing aims to exploit the features of quantum mechanics in order to solve computational tasks faster than it would be possible on classical computers. Developing this technology and understanding its capabilities is a massive and quickly evolving endeavor. A collective effort of the scientific community drawing on expertise across various disciplines is key to deliver sound and long lasting progress. Our team of mathematicians, physicists and quantum chemists will concentrate on theoretical questions central to noise-resistant quantum computation and its application to many-body theory and information processing. Answering these questions requires novel tools anchored across our different disciplines. QOMBINE brings together a unique team of experts in Norway to develop these tools. This will lay the foundations for a new and rich cross-fertilization of research in Mathematics, Physics and Chemistry in Norway. We propose a noise-based approach inspired by quantum Shannon theory to estimate quantum error correcting codes for fault-tolerant quantum computation. We propose to natively incorporate the framework of quantum groups for topological quantum computing. With twisted Fourier analysis of matrix valued maps we will improve randomized benchmarking protocols. Furthermore, we propose to apply K-theory and quantum groups to gain a thorough understanding of quantum correlations and the graph isomorphism game. By studying the coupled cluster methods from a C*-algebraic perspective, we aim to develop a unifying framework justifying these methods rigorously in special cases, and generalizing them to new cases involving particles of different braid statistics.