M.Sc. Project Assessing the expressive power of a Quantum Boltzmann Machine

Sparked by the successes of  classical Machine Learning, a new field of “quantum neural networks” is emerging. One representative of this generalization approach is the so-called Quantum Boltzmann Machine that aims at including quantum effects to improve over classical Boltzmann Machines in the learning of probability distributions. In this project you will develop analytic ansätze based on statistical mechanics techniques to infer the capability of Quantum Botzmann Machines to adapt to a class of target distributions and compare it to its classical counterpart. On this way you will learn about open quantum systems, spin glass physics and neural network models in general.

(Picture taken from: Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B., & Melko, R. (2018). Quantum boltzmann machine. Physical Review X, 8(2), 021050.)

Contact:  Lukas Bödeker, Markus Müller

M.Sc. Project Belief Propagation Decoder for Fault-Tolerant Protocols

Quantum Error Correcting Codes protect quantum information from decoherence and are an important ingredient towards fault-tolerant quantum computing. Belief Propagation is a versatile algorithm adapted from classical coding theory and is shown to work reasonably well for quantum codes using post processing methods [1]. Recently, it was adapted to handle more realistic noise models like circuit level noise [2,3]. In this project, you will learn about existing approaches to devise better decoding strategies for quantum LDPC codes, with a focus on fault-tolerant protocols.

[1] D. Poulin and Y. Chung, arXiv 1710.48550/arXiv.0801.1241 (2008),
[2] S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, arXiv 10.48550/arXiv.2308.07915 (2023),
[3]Q. Xu, J. P. B. Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasic, M. D. Lukin, L. Jiang, and H. Zhou, arXiv 10.48550/arXiv.2308.08648 (2023)

Contact:  Josias Old, Markus Müller

M.Sc. Project Finding the F-move gate representation for multicolor non-Abelian anyonic topological codes

Anyons are quasi-particles described by statistics that neither are bosons nor fermions. These particles emerge in certain 2D error-correction codes. The key to perform universal operations on non-Abelian anyonic codes is anyon fusion, splitting and braiding. When anyons fuse or split, they give rise to different anyons, whose fusion or splitting history is represented as a tree. These trees store robust logical information. Conversion between trees requires the application of a special unitary operation: the F move. It is known that for the Fibonacci code the F moves have a quantum circuit representation, but it remains unclear how to generalize this design to general non-Abelian anyonic models. In this project, you will first learn the basics of non-Abelian quantum computing, and then investigate non-Abelian anyonic models with the goal to design an F-move quantum circuit.

(Picture taken from: N. E. Bonesteel and D. P. DiVincenzo, Physical Review B 86, 165113 (2012).)

Contact:  Thiago L. M. Guedes, Markus Müller

M.Sc. Project Large language models and quantum error correction

Large language models are building blocks of advanced AI tools like chatGPT. The great power of such tools is based on exploiting hidden correlations in data. The latest is greatly accomplished by the attention based mechanism in the transformer architecture. In this project we aim to apply and develop such techniques in the framework of quantum error correction, namely decoding and circuit synthesis. Specifically, transformers may reduce the amount of syndrome measurements needed in decoding by exploiting correlation between measurements. Improvements in circuit synthesis may come from detecting correlations between gates in doing a specific task

Contact: Luis Colmenarez, Prof, Markus Müller

M.Sc. Project Implementation of quantum error correction for XZZX color codes under biased noise

The surface code is among the most studied quantum error correcting (QEC) codes, which has been implemented on systems with up to 72 physical qubits [Nature volume 614, pages 676–681 (2023)]. The recently proposed XZZX variant of the surface code [Nature Comm. 12, 2172 (2021)] has shown favorable resource scaling and high thresholds for biased noise [PRR 5, 013035 (2023)].  In this project, you will learn about QEC with color codes and investigate the performance of an XZZX version of this code on near-term quantum processors, which suffer from biased noise.

(Picture taken from Nature Comm. 12, 2172 (2021). )

Contact: Friederike Butt, Prof. Markus Müller