Open Positions
Our group offers a range of MSc projects in theoretical quantum physics with topics ranging from quantum computational optimization to the emergence of collective phenomena in non-equilibrium many-body dynamics and to projects on quantum matter in cavities. Below, please find a list of currently available projects. Feel free to contact us at any time to discuss these projects further.
Project descriptions
Master Thesis Project 1: Compressed Sensing in Quantum Computational Fluid Dynamics
Quantum algorithms for computational fluid dynamics encode flows into many-qubit wave functions. The number of function values stored in these wave functions grows exponentially with the number of qubits. Thus, the question arises, how to efficiently extract properties of flows from their quantum encoding. In this MSc project, you will utilize ideas from compressed sensing to develop methods for obtaining flow properties from quantum states. The aim is to significantly reduce the number of required measurements compared to a naïve standard approach. In the following we describe the first few steps of this MSc project in detail. Once these are complete, you will have sufficient material to write a good thesis. Ideally, a couple of months should be left to explore more advanced questions and improve the quality of your work beyond these initial points. Some possible directions for such further research are given below.
Step 1: Familiarize yourself with the basics required for this project. Read the papers [1-3] on variational quantum algorithms and [3-4] on compressed sensing [4-6] in detail. Take notes of the most important content and insights provided in these papers in preparation for writing introduction and conclusion of your MSc thesis.
Step 2: Read the publication in detail [6]. The sparse exponential pattern analysis (SEMA) explained in this paper is a form of compressed sensing. For a given multi qubit wave function, you should first reconstruct it based on measurements based on calculations. Estimate the number of measurements required as a function of the number of qubits.
Step 3: Study the paper Variational quantum algorithms for nonlinear problems [3] in detail. This explains the basic algorithm used for variationally optimizing fluid flows using the network shown in Fig. 1. The variational optimization algorithm [3] described in is achieved by measuring Ancilla qubits. Develop a plan of how this network needs to be modified to measure flow properties after successfully optimizing the flow. Estimate the number of measurements that need to be carried out for obtaining flow properties like e.g., velocity fields as a function of the number of qubits encoding the flow by using the results from Step 2.
Step 4: For given wave functions encoding flow properties (that will be provided to you) utilize the SEMA approach to measure flow properties like e.g., the velocity field or vorticity. Compare the efficiency and accuracy of SEMA to results obtained from measuring in the computational basis.
References
[1] Peruzzo, A., etc, Aspuru-Guzik, A., O’Brien, J. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 2014.
[2] Cerezo, M., etc, Coles, P., Variational quantum algorithms. Nat. Rev. Phys. 2021.
[3]. Lubasch, M., Joo, J., Moinier, P., Kiffner, M., Jaksch, D. Variational quantum algorithms for nonlinear problems. Phys. Rev. A. 101. 2020.
[4] Candès, E., Romberg, J. Tao, T. Robust Uncertainty Principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory. 52. 2006.
[5] Tran, V., Foster, M. Compressed sensing in photonics: tutorial. J. Opt. Soc. B. 40. 2023.
[6] Wang, Z., Lei, S., Karki, K., Jakobsson, A., Pullerits, T. Compressed Sensing for Reconstructing Coherent Multidimensional Spectra. J. Phys. Chem. A. 124. 2020.
Master Thesis Project 2: Compressed Sensing of Classical Data using Tensor Networks as the Sparse Representation.
Inspired by the quantum many-body and quantum information community, tensor networks reveal an outstanding ability to represent multi-dimensional data compactly. This data size compression is generally close to the idea of another powerful algorithm, compressed sensing, in the signal processing community. In this master project, we will explore the interplay between tensor network representation and the compressed sensing of data in the context of representing classical data like Fluid fields. The algorithms we develop will find relevance in a variety of tasks, including tensor network interpolation, fast compression of high-dimensional data, and fast readout in quantum-classical hybrid algorithms. [2-4]
The successful candidate will have the unique opportunity to immerse themselves in a multidisciplinary environment. This includes designing and implementing machine learning algorithms to enhance compressed sensing techniques, experimenting with quantum computing architectures, and conducting comparative studies to assess their performance in fluid dynamics scenarios.
Candidates should possess a solid foundation in quantum mechanics and matrix theory, complemented by an understanding of fluid dynamics and machine learning. Skills in programming, particularly Python and MATLAB, as well as practical experience in numerical methods for PDE resolution, are desirable.
Contact:
If you are interested and have any questions, please feel free to contact Prof. Dr. Dieter Jaksch (dieter.jaksch"AT"uni-hamburg.de); Dr. Frank Schlawin (frank.schlawin@uni-hamburg.de)(frank.schlawin"AT"uni-hamburg.de) ;Dr. Zhengjun Wang (zhengjun.wang@uni-hamburg.de)(zhengjun.wang"AT"uni-hamburg.de); Xiao Wang (xiao.wang"AT"keble.ox.ac.uk); Nis Van Hülst (nvanhuel"AT"physnet.uni-hamburg.de); Oscar Negrete (oscar.negrete"AT"uni-hamburg.de) or Belda Atilla (belda.atilla@uni-hamburg.de)(belda.atilla"AT"uni-hamburg.de)
Reference:
[1]. Jaksch, D. Givi, P. Daley, A. Rung, T. Variational Quantum Algorithms for Computational Fluid Dynamics. AIAA Journal. 61. 5. 2023.
[2]. Gross, D. Liu, Y. Flammia, S. Becker, S. Eisert, J. Quantum state tomography via compressed sensing. Phys. Rev. Lett. 105, 150401. 2010.
[3]. Candes, E., Wakin, M. An introduction to compressive sampling. IEEE Sig. Pro. 21, 2008.
[4]. Lanyon, B., Maier, C., Holzäpfel, M. et al. Efficient tomography of a quantum many-body system. Nature Phys 13, 1158–1162 (2017)
[5]. Schollwöck U. The density-matrix renormalization group in the age of matrix product states. Annals of Physics, 2011
How MSc projects work
At the start of their project students are given a project description. This will serve as an initial guide and students are expected to produce more detailed project plans during the initial phase of their project. These should be changed and updated by the student as the project evolves and new insights into the physics are gained.
The initial project description provides a list of important publications related to the topic of the project. This is usually accompanied by a set of tasks that should be completed prior to starting the actual research work and will enable students to quickly familiarize themselves with the research project.
The main part of the project is described as a set of specific tasks that can be carried out during the first half of the research project. These tasks are structured such that their successful completion will enable students to write a good quality MSc thesis.
For the majority of students, we expect that these tasks will leave plenty of time to expand the research project further and to explore additional research questions. These additional questions will often arise from the initial tasks and the study of the literature. Suggestions for possible directions for extra tasks may also be contained in the initial project description. This second part of the MSc project thus allows students to independently explore research questions and take the project into promising new directions.
The inclusion of research results arising from these additional topics will substantially strengthen any MSc thesis. In addition, we would expect to often find that such research results can be published, either as standalone publications or as part of a larger effort.
Thus, there is a good chance – but no guarantee – that an MSc project will allow students to become an author of a physics publication. The insights gained into the publishing process will be highly useful should students decide to carry on with a PhD project.
We expect most MSc students to work closely with PhD students and/or PostDocs in the group and to benefit from their research experience. In addition, MSc students will have regular meetings with Prof. Jaksch to discuss their progress and will be invited to participate in group meetings, journal clubs, etc. Please note that we are a highly international group and thus most communication within the group is in English.