Theory projects

 

Unsolicited applications

We are always happy about unsolicited applications. Please contact the principal investigator with whom you'd like to work with to discuss possible projects.

 

Berta Group
Müller Group
Hassler Group
Jülich

 

Berta Group

  Entropy and Counting Copyright: © Mario Berta

B.Sc.-Project Entropy and Counting​

In this project, you will explore mathematically the role of information theoretic ideas in combinatorial problems.

  Entropy Copyright: © Mario Berta

B.Sc.-Project Computing quantum channel capacities

In this project, you will compute numerically the ultimate limits on how well classical and quantum information can be sent over quantum channels.

  Quantum Programming in Amazon Braket Copyright: © Mario Berta

B.Sc. Project Quantum Programming in Amazon Braket

In this project, you will compile and implement proof of principle cases of state-of-the-art quantum algorithms. The Amazon Braket system is operated via Jupyter Notebooks based on Python, which are run on quantum simulators as well as various quantum processing units (see aws.amazon.com/braket/). There is the possibility to upload finished example content on the official AWS repository (upon AWS review and approval).

  Benchmarking quantum algorithms for the early fault-tolerant regime Copyright: © Mario Berta

B.Sc./M.Sc. Project Benchmarking quantum algorithms for the early fault-tolerant regime

In this project, you will compare different quantum algorithms that operate in the regime where quantum processing units feature a limited number of logical qubits. The goal is to move away from asymptotic complexities and derive finite resource estimates to assess the practicability and potential of different approaches and applications.​

  Entropy Copyright: © Mario Berta

M.Sc. Project Quantum algorithm development for the early fault-tolerant regime

In this project, you will work in the regime where quantum processing units feature a limited number of logical qubits, allowing to run small size digital schemes. You will develop and refine quantum algorithms for this regime. Via rigorous as well as heuristic complexity analyses, the goal is to single out applications with the smallest quantum resource requirements – while still showing the potential of a quantum advantage.

  Thermal State Preparation in Quantum Computing Copyright: © Mario Berta

M.Sc. Project Navier-Stokes Equations and Quantum Computing

The goal of this project is to solve the incompressible Navier Stokes equations using subroutines from quantum computing. These equations are in general nonlinear partial differential equations which are of utmost importance in continuum mechanics.
, Mario Berta

  Quantum random access memory structures Copyright: © Mario Berta

M.Sc. Project Quantum random access memory structures

Quantum algorithms operating on classical data often require coherent data access to achieve quantum speed-ups in time complexity. However, this then typically comes at the cost of exponentially large quantum space (qubit) requirements. In this project, you will study quantum error correcting codes to explore the possibility of low overhead fault-tolerant implementations of quantum data structures.

 

Müller Group

  ion trap Copyright: © Bolsmann

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 realization 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,

  circuit Copyright: © Locher

B.Sc./M.Sc. Project Multi-qubit gates with Rydberg atoms

Neutral atoms stored in optical lattices or optical tweezers form scalable quantum registers. If laser-excited to Rydberg states, these atoms exhibit strong and long-range interactions which can be exploited for the implementation of fast entangling gates between pairs and even groups of atoms. In this project, you will work on a protocol for the realization of an efficient multi-qubit Rydberg-atom entangling gate. You will perform simulations to analyze its performance, optimize it and explore how the gate can be used as a building block for quantum computing or error correction.
Contacts: , Markus Müller

  circuit Copyright: © Bödeker

B.Sc./M.Sc. Project Reinforcement learning based decoding under active leakage conversion

Many state of the art quantum error correction experiments face the problem of qubits undergoing undesired transitions out of the computational subspace - so called leakage. There are schemes to actively counteract such leakage [1]. However, the use of for instance leakage reduction units entails a complication of the error processes that take place during the experiment. To perform meaningful error correction, in this project you will construct a neural network-based decoder that will learn to counteract exotic errors by learning from the experimental data. By employing reinforcement learning as a basis for the decoder [2] you will also get insights into the underlaying error processes. Overall in this project you will get insights into quantum error correction and training neural networks (e.g. in tensorflow).
[1] Lacroix, Nathan, et al. "Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits." arXiv preprint arXiv:2309.07060 (2023).
[2] Andreasson, Philip, et al. "Quantum error correction for the toric code using deep reinforcement learning." Quantum 3 (2019): 183.

Contacts:Lukas Bödeker,

  graphene Copyright: © PRL 123, 231108 (2019)

M.Sc. Project Quantum interferometry for gravitational-wave detection

Since the detection of gravitational waves at LIGO, the field of gravitational-wave detection has witnessed an unprecedent period of expansion into interdisciplinary domains. The potential of having yet another source of information about the universe has led the quantum optics and information communities to seek for quantumly enhanced (and potentially small-scale) means for gravitational-wave detection. Following this trend, we propose to study a specific design of microscopic interferometer injected with quantum states, as an alternative to the LIGO setups. We are looking for talented students with sound knowledge of quantum mechanics and either base knowledge of field theory or eagerness to learn the topic.
Contacts: Thiago Lucena,

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

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.
Contacts: Lukas Bödeker,

  Copyright: © Old

M.Sc. Project Belief Propagation Decoders 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)

Contacts: Josias Old,

  Copyright: © N. E. Bonesteel and D. P. DiVincenzo, Physical Review B 86, 165113 (2012)

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.

Contacts: Thiago L. M. Guedes,

  Copyright: © Colmenarez

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.

Contacts: Luis Colmenarez,

  Copyright: © Old

M.Sc. Project Constructions and Performance of QLDPC Codes Tailored for Near-Term Quantum Computing Devices

Quantum Error Correcting Codes protect quantum information from decoherence and are an important ingredient towards fault-tolerant quantum computing. Promising code families are Quantum Low-Density Parity Check codes (QLDPC,) based on products of classical linear codes [1,2]. Recently, constructions that use qubit numbers that can expected to be realized in quantum computed devices in the near future have been devised [3,4].

In this project, you will learn the basics of QLDPC codes and explore the potential of existing or new construction for implementations of these codes in near term hardware.
[1] S. Bravyi and M. B. Hastings, “Homological Product Codes”, (2013) arXiv:1311.0885
[2] NP Breuckmann, JN Eberhardt, „Quantum Low-Density Parity Check Codes“, PRX Quantum, 2021
[3] S. Bravyi et al., „High-threshold and low-overhead fault-tolerant quantum memory“, (2023) arXiv:2308.07915
[4] J. Old, M. Rispler and M. Müller, „Lift-Connected Surface Codes“, (2024) arXiv:2401.02911

Contacts:Josias Old,

 

Hassler Group

  circuit Copyright: © David Scheer

B.Sc. Project Simulating dynamics of open quantum systems

For many quantum mechanical problems, the description as an isolated quantum system is not sufficient since the system is coupled to an environment. For these so-called open quantum systems, one is often interested in the effective dynamics of the system that are induced by the environment. A popular method to simulate open systems is the stochastic Schrödinger equation that accounts for quantum jumps in the form of measurements performed by the environment. In this project, you will implement simulations of a stochastic Schrödinger equation and compare the method to other common approaches such as the Lindblad master equation.
Contacts: , Fabian Hassler

  Setup Copyright: © Steven Kim

B.Sc. Project Removing unphysical effects in the simulation of non-Hermitian systems

In a realistic setting, quantum systems interact with their environment, e.g., via emission or absorption of photons. These so-called open quantum systems have to be described by non-Hermitian operators and matrices. To simulate non-Hermitian bosonic systems, it is necessary to introduce a cut-off to the dimension of the Hilbert space. However, the spectrum and the quantum states change depending on the truncation method. Additionally an accumulation of states at the boundary of the Hilbert space is possible, also known as the non-Hermitian skin effect. The goal of this thesis is to solve the problems listed above and find a basis where these unphysical effects do not appear.
Contacts: , Fabian Hassler

  Detector setup Copyright: © Fabian Hassler

M.Sc. Project Detector theory for microwave photonics with superconducting quantum circuits

In superconducting quantum systems, a significant part of the emitted microwave radiation can be collected and converted to an amplified output signal. This allows for a detailed study of the correlations of the radiation. The statistics of the radiation can offer a valuable insight into the quantum nature of the radiation. It demonstrates phenomena like squeezing or multi-photon processes. In order to study such phenomena theoretically, it is necessary to develop a fitting model for the detector. The goal of this project will be to explore different theoretical detector models for microwave photonics, including the initial detection of the photons, the amplification of the signal, and possible backaction due to the detector.
Contacts: , Fabian Hassler

 

Jülich Institute

  Setup Copyright: © Mohammad H. Ansari

M.Sc. Project Quantum Machine Learning, Circuit QED, Quantum Thermodynamics

You will conduct research on either one of these topics: 1) Quantum Machine Learning: You learn how to perform techniques such as neural networks on quantum physics and chemistry problems; 2) Circuit QED: You will learn how to couple qubits in a circuit and how to make quantum processors, theoretically; 3) Quantum Thermodynamics: You will learn how to alter heat engine, e.g. solar cells, Photosynthetic systems etc., by adding small quantum elements they perform differently.
​Contact:

  Flux Qubit Copyright: © Gianluigi Catelani

B.Sc. and M.Sc. Projects Superconducting Qubits

In these projects you will study theoretically some basic properties (energy levels, wave functions, matrix elements) of superconducting qubits such as the fluxonium and the flux qubit. These properties can be accurately calculated numerically in most cases, especially if the problem reduces to that of a quantum particle in a one-dimensional potential. The goal here is to construct an approximate but accurate analytical solution to such a quantum-mechanical problem, using perturbation theory, the WKB approximation, etc. For a B.Sc. project, a symmetric double-well potential will be analyzed. Extension of the results to asymmetric potentials, and to two- or three-dimensional problems, can be considered for a M.Sc. project. Contact: Gianluigi Catelani (g.catelani@fz-juelich.de)