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FRINATEK-Fri prosj.st. mat.,naturv.,tek

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

Alternative title: Matematikk for kvanteberegning og mangelegemeteori (QOMBINE)

Awarded: NOK 12.5 mill.

Quantum computing is an impending technology with a huge potential to solve important societal and business problems. When compared to classical computers, quantum computers can dramatically speed up processing time for some specific tasks, for example in quantum chemistry. This could impact different sectors of industry such as the food-, chemical-, and pharmaceutical industries. However, before the potential of quantum computing can be realized, major theoretical and technological obstacles need to be overcome. At center stage is the problem that the components of a quantum computer inadvertently interact with each other and the environment. This is undesirable since one can only perform short and imperfect calculations. At present there is a limited number of cases for which existing quantum computers outperform classical computers. The focus of the project is three-fold. Firstly, we will develop new mathematical methods to benchmark, detect, suppress, and correct the errors in quantum computers stemming from the interaction with the environment. This will contribute to realizing the potential advantage of quantum computers. Secondly, we will devise a unified mathematical framework that can be applied to a wider range of applications within the area of quantum chemistry. Quantum chemistry is a field that deals with predictions of properties of molecules and materials. Finally, we will study non-classical features of quantum mechanics that enable quantum encrypted communication. We will find new formulas to quantify the performance of these encryption methods under the interaction with the environment.

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.

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FRINATEK-Fri prosj.st. mat.,naturv.,tek