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Title of the thesis: Reinterpreting tensor networks: quantum-inspired solutions to problems in condensed matter physics

Thesis defender: Marcel Niedermeier
Opponent: Dr. Christoph Groth, CEA (French Atomic Energy Commission) 
Custos: Prof. Jose Lado, Aalto University School of Science

Many problems in the physical sciences are hard. For instance, if we wish to model the behaviour of a given material by describing it at the atomic level, the number of parameters to keep track of typically scales exponentially with the number of atoms taken into account. Even with current supercomputers, performing such simulations exactly is thus only possible for the smallest of systems. On the other hand, research in recent decades has shown that it is typically not necessary to keep track of all of these parameters. Physical systems exhibit structures; they are not random – and structure implies compressibility. Akin to the compression of images, we may use similar tools, so-called tensor networks, to compress quantities like quantum states, allowing us to perform quantum simulations at much greater scales than previously thought possible.

Another avenue currently pursued to achieve certain computations much faster is quantum computing. In the context of physics, it would allow us to simulate quantum systems directly with other quantum systems, but also offers sizeable advantages for other computational tasks, such as database search. However, practical implementations of quantum computers remain prone to errors and cannot yet operate at the scales required to tackle today’s most complicated problems.

In this thesis, we bring together tensor network techniques and quantum computing, and showcase how they complement each other. Both can be used to simulate the same problems, and tensor networks can be used to better understand fundamental properties of quantum algorithms themselves - if we can simulate a given quantum algorithm, its promised advantage may not be as significant as imagined. Furthermore, this interplay has given rise to a new class of recently emerged algorithms, “quantum-inspired” algorithms, which use ideas from quantum physics to highlight scales and structures in conventional numerical computations. In summary, many numerical calculations may not be as hard as once thought, and we now possess a toolbox with tensor networks, quantum-inspired techniques and quantum computing to tackle them. All of these form an exciting interplay, with each pushing the boundaries of the others. 

Keywords: quantum computing, tensor networks, matrix product states, quantum-inspired algorithms

Contact information: marcel.niedermeier@aalto.fi or  

Thesis available for public display 10 days prior to the defence at .