B.Sc. Project Quantum Processing with Trapped Rydberg Ions

Trapped Rydberg ions are a promising novel emerging physical platform to build quantum computers and simulators. Here, trapped ions are laser-excited to Rydberg states, where they behave as a composite object and exhibit strong and long-range interactions, which enable the realisation of fast quantum gate operations and quantum simulation of many-body spin models. In this project, you will theoretically model Rydberg ions in a Paul trap and use analytical techniques as well as numerical methods (such as Lindblad quantum master equations) to develop protocols and study the performance of quantum gate operations and building blocks for quantum error correction in this system.

Contact: Katrin Bolsmann, Markus Müller

M.Sc. Project: Discover local decoders via neural cellular automata

Scalable decoding is an essential ingredient for large-scale fault-tolerant quantum computation [1]. To execute complex algorithms, we require high-precision logical qubits protected by large-scale Quantum Error Correction (QEC) codes. Local decoders are prime examples of scalable decoders; because they rely only on neighborhood information, their cycle time does not scale with the code size.

In this project, we explore local decoding for stabilizer codes using Neural Cellular Automata (NCA). Inspired by recent advances in trainable CA [2-4], we will develop a framework to discover local rules based on syndrome data. We begin by validating the framework on the repetition code to see if the NCA can rediscover or improve upon known CA decoders [5]. We then extend this to more complex codes and, if time allows, include constraints such as rule partitioning. This final step aims to elevate classical CA rules to Quantum Cellular Automata (QCA) [6, 7], potentially enabling scalable and measurement-free QEC.

[1] A. G. Fowler et al., Phys. Rev. A 86, 032324 (2012).
[2] A. Mordvintsev et al., Distill (2020).
[3] E. Pajouheshgar et al., arXiv:2412.15187 (2024).
[4] P. Miotti, et al., arXiv:2506.04912 (2025).
[5] L. Paletta, et al., arXiv:2505.06453 (2025).
[6] T. Farrelly, Quantum 4, 368 (2020).
[7] T. L. M. Guedes, et al., Phys. Rev. Lett. 133, 150601 (2024).

Contact: Don Winter, Markus Müller

M.Sc. Project: Investigating magic state distillation protocols via dynamical maps

To achieve universal fault-tolerant quantum computation, one needs to implement logical non-Clifford gates, which are usually more challenging than logical Clifford gates within quantum error-correcting codes. Several approaches have been developed to realize logical non-Clifford gates fault tolerantly. One of the most promising is the distillation of high-fidelity resource states, known as magic states [1], which can then be consumed using Clifford circuits to implement non-Clifford gates.

Several key properties of magic state distillation protocols can be analyzed by mapping them to dynamical maps [2,3]. In this project, you will use these techniques to investigate the robustness of magic state distillation protocols under realistic noise models and potentially develop new circuits or protocols that exhibit improved performance in such settings.

[1] S. Bravyi and A. Kitaev, Phys. Rev. A 71, 022316 (2005)
[2] Y. Zheng and D. E. Liu, Quantum 9, 1858 (2025)
[3] Y. Zheng, Y. Zhao and D. E. Liu, arXiv:2503.01165 (2025)

Contact: Aron Marton, Markus Müller

M.Sc. Project: Constructing quantum error-correcting codes from Majorana graphs

Quantum error-correcting codes are essential for protecting quantum information against environmental noise. One of the most widely studied families of such codes are surface codes. The logical states of surface codes can be understood by mapping a system of Majorana fermions defined on a planar graph to a system of qubits [1,2,3]. This mapping provides a clear interpretation of the logical degrees of freedom of planar surface codes: twist defects can be associated with unpaired Majorana modes. Moreover, certain logical operations admit a natural interpretation in terms of braiding and measurement of these logical Majorana fermions [4].

In this project, you will generalize this construction to other, possibly higher-dimensional, quantum error-correcting codes by defining new classes of Majorana graphs and mapping them to qubit systems. The focus will be on understanding which logical operations can be realized within this framework, as well as exploring other potentially interesting properties of these newly constructed codes.

[1] S. Bravyi et al. npj Quantum Information 4, 55 (2018)
[2] F. Venn and B. Béri, Phys. Rev. Research 2, 043412 (2020)
[3] R. Sarkur and T. J. Yoder, Quantum 8, 1416 (2024)
[4] Y. D. Lensky et al. Annals of Physics 452, 169286 (2023)

Contact: Aron Marton, Markus Müller

B.Sc/M.Sc. Project: Experimentally informed decoding of quantum error-correcting codes

The error detection capabilities of quantum error-correcting codes are captured by detector error models, in which error mechanisms trigger one or more detectors. The resulting pattern of detector violations constitutes the experimentally accessible syndrome information in quantum error correction experiments. Given a detector error model and an observed syndrome, a decoding algorithm can be applied to infer a likely set of error mechanisms responsible for the observed syndrome.

In real quantum error correction experiments, however, the underlying error mechanisms are not known a priori. Instead, the detector error model can be reconstructed directly from experimentally measured syndrome statistics [1–3]. When such models contain hyperedges—corresponding to error mechanisms that trigger more than two detectors—decoding becomes more challenging. In this project, you will investigate methods to reconstruct detector error models without hyperedges from experimental data and evaluate how effectively these simplified models can be used for decoding.

[1] S. T. Spitz et al. Adv. Quantum Technol., 1, 1800012 (2018)
[2] A. Remm et al. arXiv:2502.17722
[3] E. Takou and K. R. Brown, Phys. Rev. A 112, 052414 (2025)

Contact: Aron Marton, Markus Müller