Abschlussarbeiten

Doktorarbeiten

• Michael Zurel, Classical descriptions of quantum computations : foundations of quantum computation via hidden variable models, quasiprobability representations, and classical simulation algorithms, 2024 (betreut von Robert Raußendorf)
• Oleg Kabernik, Reductions in finite-dimensional quantum mechanics : from symmetries to operator algebras and beyond, 2021 (betreut von Robert Raußendorf)

Masterarbeiten

• Ryohei Weil, Quantifying resource states and efficient regimes of measurement-based quantum computation on a superconducting processor, 2024 (betreut von Robert Raußendorf)
• Luis Mantilla Calderon, Measurement-based quantum machine learning, 2023 (betreuet von Dmytro Bondarenko, Polina Feldmann, Robert Raußendorf)
• Arnab Adhikary, Symmetry protected measurement-based quantum computation in finite spin chains, 2021 (betreut von Robert Raußendorf)
• Paul Herringer, Classification of quantum wire in tensor network states with a local Pauli symmetry, 2021 (betreut von Robert Raußendorf)
• Michael Zurel, Hidden variable models and classical simulation algorithms for quantum computation with magic states on qubits, 2020 (betreut von Robert Raußendorf)
• David Stephen, Computational power of one-dimensional symmetry-protected topological phases, 2017 (betreut von Robert Raußendorf)

Bachelorarbeiten

• Elektra Dakogiannis, Coherent Noise Models in Concatenated Stabilizer Codes, 2023 (betreut von Gabrielle Tournaire, Robert Raußendorf)
• Julian Ding, Simulation of the Kitaev planar code error threshold under a photonic local error model, 2022 (betreut von Robert Raußendorf)
• Ryohei Weil, A Simulation of a Simulation : Algorithms for Symmetry-Protected Measurement-Based Quantum Computing Experiments, 2022 (betreut von Robert Raußendorf)
• Aslan Zhang, Compilation Optimization for Measurement-based Quantum Computation on Graph States, 2022 (bereut von Polina Feldmann, Robert Raußendorf)

Doktorarbeiten

• Solving separability problems with machine learning (contact: Martin Plávala)

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  Detecting quantum entanglement is a hard task: while some computable criteria exists, they may not be sufficient or may be impossible to compute beyond the smallest local dimensions of the underlying Hilbert spaces. A potential solution is offered by machine learning where various methods were used to classify separable and entangled states. These methods have their own pitfalls: they usually only predict whether the state is separable or entangled with some probability, but there is no way to verify this prediction or to estimate the noise-robustness of the entanglement.
  
  This project aims to rectify all of these problems: the aim is to construct entanglement witnesses from a large class corresponding to a fixed level of the hierarchy of symmetric extensions; these entanglement witnesses are known to perform reasonably well in applications and they have favorable computational properties in that they can be numerically verified to be entanglement witnesses. Deep neural networks will be used to construct these entanglement witnesses; since the neural network will be guessing entanglement witness from the specific class, the result will be verifiable in that if entanglement is detected, explicit witness will be provided as well. The goal of the project is to make these methods work for high-dimensional cases where other methods fail due to a lack of computational resources.
  
  As a follow-up project, the developed methods will be applied to high-dimensional steering and Bell nonlocality, since both of these problems are known to be analogical to separability and the developed methods will directly generalize to these cases. Further projects will include improving the performance of the machine learning methods and investigating nonlocality in the triangle network, the later will present a novel set of challenges since the underlying problem is not linear (unlike all of the previous problems).
  
  The ideal candidate should have background in linear algebra and interest in quantum information, previous experience in machine learning and deep neural networks is welcome. The project will involve mainly developing and testing various machine learning models constructing the entanglement witnesses, the necessary mathematical calculations will likely involve only undergraduate level linear algebra and quantum information and relevant numerical methods. Thus all candidates should have interest in programming and numerical mathematics.

Masterarbeiten

• k-compatibility of channels in general probabilistic theories (Ansprechperson: Martin Plávala)

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  General probabilistic theories (GPTs) are a class of theories that include both classical and quantum information as well as other mathematically consistent theories. GPTs are a point of interest in quantum foundations when attempting to derive quantum theory, but they are also used in quantum information to reformulate and solve problems. A channel is a transformation of the states of the system, such as for example time evolution for a given amount of time. A set of channels is k-compatible if given k exact copies of the input state, there exist another channel that outputs a state that is locally identical with outputs of all of the considered channels. The goal of the project is to investigate when a set of channels is k-compatible within a given GPT, special attention will be put on connecting k-compatibility of several instances of the identify channel and geometric properties of the considered state space. The project will mostly involve only analytic methods and will be close to mathematical research.

• Products of POVMs (Ansprechperson: Martin Plávala)

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  POVMs are a mathematical representation of the measurement devices in quantum information. Most notably a set of POVMs can be compatible or jointly measurable, meaning that all of the measurements represented by the respective POVMs can be reduced to only a single measurement. The goal of the project is to investigate when for compatible POVMs the single measurement can be constructed using some notion of operator product, what are the properties of such operator products and whether they have any operational meaning. The project will mostly involve analytic methods with some numerics to construct appropriate examples.

• Quantum solutions to linear constraint systems - combining contextuality and symmetry (contact: Markus Frembs)

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  Quantum and classical mechanics are built on fundamentally different mathematical structures. Making precise these differences is a key effort towards a better formal understanding and interpretation of quantum theory, which moreover plays a central role in the theoretical development of quantum computing and information science.
  The prime example for this is Bell nonlocality [1], as exhibited by quantum entanglement: the impossibility to describe quantum correlations within the realms of classical physics - the experimental verification of which has recently been awarded the Nobel Prize in Physics [2] - is one of the main driving forces for the development of quantum computers. Contextuality - roughly the impossibility to assign quantum observables definite outcomes prior to experiment - marks another point of departure from classical physics [3], which has also been identified as a fundamental resource for quantum advantage in different architectures of quantum computation [4]. However, unlike the theory of entanglement the mathematical structure of contextuality remains much less developed.
  This project aims to study contextuality using symmetry, more specifically, (discrete) symmetry groups of Euclidean spaces in low dimensions. The central goal is to (computationally) search for and formally describe quantum solutions to linear constraint systems for qudit systems [5], thus generalising similar examples for qubits [6]. In addition, the project aims to develop a group-theoretic description of contextuality, building on recent work in Ref. [7].
  The project would suit someone who is interested in quantum foundations, enjoys to work on problems in mathematical physics, has a background in group theory and some minimal coding experience.
  
  [1] J. S. Bell, On the Einstein-Podolsky-Rosen Paradox, Physics 1 (1964), 195
  [2] https://www.nobelprize.org/prizes/physics/2022/summary/
  [3] S. Kochen, E. P. Specker, The Problem of Hidden Variables in Quantum Mechanics, J. Math. Mech. 17 (1967), 59-87
  [4] R. Raussendorf, Contextuality in measurement-based quantum computation, Phys. Rev. A 88 (2013), 022322; M. Howard et al, Contextuality supplies the ‘magic’ for quantum computation, Nature 510 (2014), 351-355
  [5] R. Cleve, L. Liu, W. Slofstra, Perfect commuting-operator strategies for linear system games, J. Math. Phys. 58 (2017), 012202
  [6] N. D. Mermin, Simple unified form for the major no-hidden-variables theorems, Phys. Rev. Lett 65 (1990), 3373-3376; N. D. Mermin, Hidden variables and the two theorems of John Bell, Rev. Mod. Phys. 65 (1993), 803-815
  [7] M. Frembs, C. Okay, H.-Y. Chung, No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords, Quantum 9 (2025), 1583

Bachelorarbeiten

Doktorarbeiten

• Arnab Adhikary, Computational phases of quantum matter — Korrelationen verstehen (betreut von Robert Raußendorf)
• Ruben Campos Delgado, Quantenfehlertoleranz — Effiziente Quantencodes (betreut von Robert Raußendorf)
• Poya Haghnegahdar, Messungsbasiertes Quantenrechnen auf Affleck-Kennedy-Lieb-Tasaki Zuständen (betreut von Robert Raußendorf)
• Lukas Hantzko, Computational phases of quantum matter — Algebraische Struktur (betreut von Robert Raußendorf)
• Paul Herringer, Computational phases of quantum matter — Verbindungen mit der Physik kondensierter Materie (betreut von Robert Raußendorf)
• Thierry Kaldenbach, Graphenzustände und Quantenalgorithmen (betreut von Robert Raußendorf)
• Marvin Schwiering, Quantenrechner—Architektur (betreut von Robert Raußendorf)
• Gabrielle Tournaire, Fehlertolerantes Quantenrechen mit topologischen Quantencodes (betreut von Robert Raußendorf)

Masterarbeiten

• Niko Trittschanke, Handling Quantum Errors under Realistic Noise Models for Trapped Ion Quantum Devices (betreut von Robert Raußendorf)

Bachelorarbeiten