# Theoretische Arbeiten

## Initiativbewerbungen

Wir freuen uns immer sehr über Initiativbewerbungen. Bitte kontaktieren Sie hierzu den Gruppenleiter, mit dem Sie arbeiten möchten, um mögliche Projekte zu besprechen.

B.Sc.-Arbeit** **
**Bosonic quantum error correction with trapped ions**

Trapped ions are one of the leading platforms to build robust quantum information processors. Instead of storing information in electronic qubit-states, it has recently been shown that vibrational modes of trapped ions can be used to encode and protect quantum information in bosonic quantum error correction codes, such as Schrödinger cat codes or the GKP code. In this project, you will analyse and numerically simulate such a code, and among other methods use Lindblad master equations to gain insight into the creation, dynamics and stabilisation of such states in realistic trapped-ion setups.

Contact: Markus Müller

M.Sc.-Arbeit** **
**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.

Kontakt: Mario Berta

B.Sc./M.Sc.-Arbeit** **
**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.

Kontakt: Mario Berta

B.Sc.-Arbeit** **
**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).

Kontakt: Mario Berta

M.Sc.-Arbeit **Thermal State Preparation in Quantum Computing**

Preparing thermal states is a fundamental task for quantum algorithms. Thinking from a classical approach, this generalises the idea of classical Gibbs samplers. The goal of this project is to implement state-of-the-art quantum algorithms numerically and to make a directed comparison to classical methods.

Kontakt: Gereon Kossmann, Mario Berta

M.Sc.-Arbeit **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.

Kontakt: Gereon Kossmann, Mario Berta

B.Sc./M.Sc.-Arbeit **Alternating entropic optimization**

In quantum communication and learning theory many fundamental quantities of interest are given by entropic optimization programs. Consequently, basic open questions in quantum information theory are linked to a better understanding of entropic optimization programs. In this project, you will refine and benchmark methods to compute convex as well as non-convex instances of entropic optimization programs.

Kontakt: Mario Berta

M.Sc.-Arbeit **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.

Kontakt: Mario Berta

B.Sc.-Arbeit** **
**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 devise a protocol for the realisation of an efficient multi-qubit Rydberg-atom entangling gate, use analytical techniques and simulations to analyse its performance, and explore how this can be used as a building block for quantum computing or error correction.

Contacts: David Locher, Markus Müller

B.Sc./M.Sc.-Arbeit** **
**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: Markus Müller

M.Sc.-Arbeit** **
**Topological Quantum Error Correction**

Topological quantum error correcting codes provide a mathematically elegant and practically highly promising approach to fight errors in scalable quantum computers. In this project, you will familiarise yourself with such quantum codes, and use analytical tools and numerical simulations to assess their performance under realistic noise.

Contact: Markus Müller

B.Sc./M.Sc.-Arbeit** **
**Constructing fault-tolerant quantum circuits with Boolean logic**

Fault-tolerant operation of quantum computers relies on logical building blocks which manipulate the logical information stored in a quantum error correcting code in a way that prevents uncontrolled spreading of errors beyond a tolerable amount. This project aims at contructing fault-tolerant gadgets with the help of classical boolean logic. Your goal will be to implement fault tolerance constraints into methods to systematically find quantum circuits to realize given logical operations.

Contacts: Sascha Heußen, Markus Müller

B.Sc./M.Sc.-Arbeit** **
**Variational Quantum Algorithms applied to Condensed Matter and Quantum Chemistry problems**

In the era of noisy intermediate scale quantum computers, hybrid algorithms that combine classical and quantum resources are of great interest. Variational Quantum Algorithms (VQEs) are among the most successful hybrid algorithms today. This family of algorithms optimize a cost function (e.g. energy of a Hamiltonian) using a classical algorithm but computing and optimizing the cost function value using a quantum computer. In this project we are going to develop circuit ansatze and strategies for solving problems related to quantum chemistry and condensed matter physics.

Contacts: Luis Colmenarez, Markus Müller

M.Sc.-Arbeit **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, Markus Müller

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, Markus Müller

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, 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.

Contacts: 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.

Contacts: Luis Colmenarez, Markus Müller

M.Sc. Project **Fault-tolerant universal quantum computation by concatenation and distillation**

Recent improvements on magic state distillation schemes enable to create high-fidelity magic state with less qubit overhead than previously thought. Applying few-qubit magic state distillation schemes [arXiv:2112.01446 and arXiv:1204.4221/1811.00566] to logical qubits encoded in small-distance codes may be compatible with current or near-future experimental quantum computing hardware. In this project, you will investigate the fault tolerance properties of such concatenated schemes and analyze their usefulness for practical applications.

Contacts: Sascha Heußen, 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.

Contacts: Friederike Butt, Markus Müller

M.Sc.-Arbeit** 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: Dr. Mohammad H. Ansari

B.Sc.-Arbeit** **
**Effects of quasiparticle poisoning on dual Shapiro steps**

A superconducting phase slip junction can exhibit steps of constant current in its IV-characteristic.

These so-called dual Shapiro steps relate current to frequency which has important applications in the

field of quantum metrology. In a realistic device, quasiparticles can enter the junction modifying its

electrical properties. This introduces noise in the device that decreases the visibility of the steps. In

this project, you will develop an analytical understanding of dual Shapiro steps and perform numerical

simulations to determine the effect of quasiparticle poisoning on the step-width.

Contacts: David Scheer, Fabian Hassler

B.Sc.-Arbeit** Efficient Simulation of the Lindblad Equation**

Open quantum systems interact with their environment e.g., via emission or absorption of photons. The equation governing the dynamics of these system is called the Lindblad master equation which takes the interaction into account and can be used to study e.g., electronic quantum circuits. Solving the equation gives insight into possible instabilities, phase transitions and enables the study of the cumulants of observables such as the photon current. In this thesis, you will develop an algorithm to solve this equation numerically and compare the outcome to analytical results.

Contacts: Steven Kim, Fabian Hassler

B.Sc.-Arbeit** Chiral anomaly in 1D**

Chiral anomaly describes the process where for a system of chiral fermions (massless Dirac equation), the particle number of the right movers are not conserved. Applying a time-dependent electric field, particles are "created out of the vaccuum". In this project, you will numerically simulate this physics by simulating the time-dependent Schrödinger equation of a system of non-interacting fermions (fermi sea). You will compare the numerical results to the analytical predictions obtained by field theory or bosonization.

Contacts: Fabian Hassler

M.Sc.-Arbeit** 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: David Scheer, Fabian Hassler

B.Sc.-Arbeit** Hall Effect Gyrator**

This work will continue recent investigations in our group on the action of an essential component in quantum microwave science, the gyrator. Here you will do calculations of the real-time propagation of electromagnetic fields in this device. Contact: David DiVincenzo

Urheberrecht: © Pascal CerfontaineB.Sc.-Arbeit** Improved Quantum Dot Qubits**

In this project you will explore theoretically variants of the semiconductor quantum dot to perform quantum gate fidelity and readout. There will be an emphasis on tailoring the spin-orbit action to achieve optimal performance, and on varying the electron number and confinement strength. Contact: David DiVincenzo

Urheberrecht: © 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)