# 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.

B.Sc. Project **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

B.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 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. Project **A machine learning approach for the decoding of topological error correcting codes**

Machine learning and neural networks are successfully employed for a variety of tasks in industry and research. In quantum error correction one faces the task to identify and counteract errors based on incomplete measurements of an ensemble of qubits in order to preserve the stored quantum information. In this project you will simulate topological codes numerically and work with neural network implementations to perform error correction on them. Further you will explore methods to interpret the decision making of the neural network in the context of fault tolerance.

Contacts: Lukas Bödeker, Markus Müller

B.Sc. Project **Solving NP-hard problems with Gaussian boson sampling**

Boson sampling is a quantum computing technique that makes use of sampling from the symmetric wavefunction that bosonic systems have. States with Gaussian-shaped Wigner functions are used as input states into a photonic quantum computing device. GBS has recently become a second platform to show quantum computational supremacy over classical algorithms. In this project, you will explore problems to which GBS offers a computationally efficient solution by sampling from the Hafnian function of a matrix, e.g. a graph’s adjacency matrix.

Contacts: Sascha Heußen, Markus Müller

B.Sc. Project **Efficient sampling of experimentally relevant quantum error correcting circuits**

Simulating faulty gate operations in stabilizer codes poses numerical challenges to keep up with the experimental scale-up of quantum hardware to large qubit systems with high fidelity operations. In this project, you will apply and adapt the dynamical subset sampling algorithm to QEC circuits used for fault-tolerant quantum hardware to efficiently extract feasibility information of different routes for experimental progress in the field.

Contacts: Sascha Heußen, Markus Müller

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: Dr. Mohammad H. Ansari

Copyright: © Phys.Rev. B 84, 041404(R)(2011)

B.Sc. Project **Magnetic moments in strained bilayer graphene**

Implementing a strain in bilayer graphene has been shown to result in massive low-energy modes at the corners of the Brillouin zone [Phys.Rev. B **84**, 041404(R)(2011)]. In this thesis, you will investigate the effective low-energy Hamiltonian analytically. You will learn about berry curvature and how it relates to a formulation of a magnetic moment for these massive modes. Subsequently, you construct wavepakets and study their response to magnetic fields to develop an intuition of the effects of this so called topological magnetic moment.

Contacts: Alexander Ziesen, Fabian Hassler

Copyright: © arXiv:2106.01909

B.Sc. Project **Supercurrent diode effect**

Usually, pairing mechanisms in superconductors couple electrons into Cooperpairs of zero total momentum. This leads to direction independent critical currents of the superconductor. However, for so-called two dimensional helical superconductors, which can be described by a two dimensional electron gas with spin-orbit coupling, an in-plane magnetic field, introduced via a Zeeman term, leads to a pairing mechanism producing finite Cooperpair momentum. At the heart of this effect, is the topologically non-trivial spin structure of the Fermi surface. For these helical superconductors, the critical current, also called depairing current, that leads to a break-down of superconductivity is spatially asymmetric. The theoretical investigation of this superconducting diode effect and how it could be detected in measurements is the topic of this thesis.

Contacts: Alexander Ziesen, Fabian Hassler

Copyright: © Lisa Arndt

B.Sc. Project **Period tripling due to parametric down-conversion**

Discrete time-translation symmetry breaking can be observed in periodically-driven systems oscillating at a fraction of the frequency of the driving force. This property has been attracting much attention recently in the context of discrete time crystals. In this thesis, you will employ analytical and numerical methods to investigate a Duffing oscillator which is parametrically driven at three times its resonance frequency and compare your results to an oscillator that is stabilized by a Josephson potential.

Contacts: Lisa Arndt, Fabian Hassler

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: Lisa Arndt, Fabian Hassler

Copyright: © David DiVincenzo

B.Sc. Project

**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

Copyright: © Pascal Cerfontaine

B.Sc. Project **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

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)