Department of Physics
Point defects in semiconductors for quantum technologies
Defects are flaws in the crystal structure of semiconductors. These flaws can be missing atoms, or an atom sitting in the wrong place in the crystal. Such defects are interesting because they can change how a semiconductor material conducts electricity or absorbs and emits light. Without these defects, we actually would not have the electrical components we know today, such as computers, solar cells and sensors, but they are only a benefit when we introduce them on purpose. When they are introduced to the material accidentally, they can destroy the properties we hope to exploit. In our research, we therefore aim to understand and control semiconductor defects, so that they are only introduced when and where we want them to be.??
The topic of this group of master projects is?how to understand and?use?point defects in semiconductors for quantum technology (QT) applications.?Certain point defects can be used as building blocks for QT. Such point defect quantum bits, or qubits, can be used for quantum sensing, communication and computing. We are particularly interested in using point defects for quantum sensing.?
Project 1: Theoretical modeling of point defects in semiconductors for quantum technologies
Supervisor: Assoc. Prof. Marianne E. Bathen
Project description: In this type of master project, you will use large-scale simulation frameworks to model the behavior of semiconductor materials and defects embedded within them. Relevant projects include machine learning prediction of novel semiconductor defect hosts, explorative studies of new defect candidates for color centers, and in-depth studies of defect properties such as formation energy diagrams, emission line energies and phonon interactions.
Methodology for master project: Theoretical modeling using density functional theory (DFT)
Prerequisite knowledge:
FYS2140 – Quantum Physics FYS3280 – Semiconductor Components FYS3400 – Condensed Matter Physics and Quantum Materials
Recommended courses to take during first semesters of master programme:
Project 2: Defect characterization for quantum technologies
Supervisor: Assoc. Prof. Marianne E. Bathen
Project description: In this type of master project, you will work experimentally to study the properties and behavior of semiconductor point defects. A particularly interesting angle is their response to external perturbations, such as temperature, pressure and electromagnetic fields, towards quantum sensing applications.
Methodology for master project: Defect characterization (e.g., photoluminescence, deep level transient spectroscopy).
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project 3: Material growth and characterization for quantum technologies
Supervisor: Prof. Lasse Vines
Project description: In this type of master project, you will work experimentally to study the growth of novel materials, such as nitrides, to act as hosts for semiconductor defects for quantum technologies.
Methodology for master project: Material deposition techniques (e.g., sputtering), material characterization techniques (e.g., XRD, photoemission) or defect characterization (e.g., photoluminescence, deep level transient spectroscopy).
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project 4: Nanostructuring for defect based quantum technologies
Supervisor: Prof. Lasse Vines
Project description: In this type of master project, you will work experimentally to develop micro- and nanostructures in semiconductors for electronic and photonic device integration of color centers.
Methodology for master project: Micro- and nanofabrication (e.g., photolithography, deposition, etching), device characterization (e.g., scanning electron microscopy, electrical measurements)
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Computational quantum technologies
Project 5: Theoretical studies of spin qubits in quantum dot systems
Supervisor: Prof. Morten Hjorth-Jensen
Project description: In this type of master project, you will work on many-body theories for the realization of various quantum gates for spin qubits in quantum dot systems. This includes studies of entanglement, superposition and interference, error mitigation, quantum sensing, and other fundamental quantum mechanical properties.
Methodology for master project: Quantum mechanical theories for many-particle physics, time-dependent many-body methods, quantum computing and quantum technologies, computational physics and science and data science.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project 6: Quantum machine learning
Supervisor: Prof. Morten Hjorth-Jensen
Project description: In this type of master project, you will work on classical and quantum machine learning algorithms applied to simulation of physical systems on quantum computers, using both classical data sets and quantum mechanical data sets.
Methodology for master project: Quantum mechanical theories, machine learning, quantum machine learning, reinforcement learning and quantum reinforcement learning.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
FYS4110 – Advanced Quantum Mechanics FYS4480 – Quantum mechanics for many-particle systems FYS-STK4155 – Applied Data Analysis and Machine Learning
Project 7: Physics-inspired quantum algorithms
Supervisor: Prof. Morten Hjorth-Jensen
Project description: In this type of master project, you will work on the development of physics inspired quantum algorithms for the simulation of quantum mechanical many-particle systems on existing quantum computers like LUMIQ (Finland) and QuNorth (Denmark) . This includes studies of how to initialize systems on quantum computers, studies of their time evolution and final measurement. Applications will focus in particular on quantum sensing for spin qubits.
Methodology for master project: Quantum mechanical theories for many-particle physics, time-dependent many-body methods, quantum computing and quantum technologies, computational physics and science and data science.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Physics of quantum circuit elements
Project 8: Physics of assemblies of Josephson junctions
Supervisor: Prof. Olav F. Sylju?sen (Theoretical physics)
Project description: The Josephson junction is the essential ingredient in a superconducting qubit. In this project you will study the physics of assemblies of coupled Josephson junctions with the goal of theoretically predicting/explaining results of experiments.
Methodology: Computational physics methods: Monte Carlo methods, exact diagonalization, Langevin simulations , and/or )dependent on the interest of the candidate): Analytical methods from statistical mechanics.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
FYS4110 – Advanced Quantum Mechanics FYS4430 – Condensed Matter Physics II FYS4480 – Quantum mechanics for many-particle systems
Quantum materials
Relativistic quantum information
Project 8: Local measurements and locally equivalent states in quantum field theory
Supervisors Jan Gulla, Prof. Johannes Skaar (Theoretical physics)
In quantum information technology, it is crucial to be able to generate signals on demand in order to describe transfer of information. Such states must be locally equivalent to some background state outside the light cone of the trigger. It is of interest both to understand this equivalence, and more fundamentally, to understand local operations and measurements in quantum field theory (QFT).
Possible master's thesis topics include:
Local measurements and operations in QFT. What exactly are local measurements and quantum operations in QFT? What is the state-update rule post measurement in QFT? How to settle Sorkin's scenario?
Local equivalence: two states are said to be locally equivalent in X, if they predict the same measurement statistics for all local measurements in X. Develop the theory of equivalence for (possibly mixed) states, and consider the relation to explicitly time-dependent processes.
For both topics the work will involve mathematical analysis (pen-and-paper), possibly with some analytical computer tools and/or numerics.
Department of Mathematics
Quantum information theory
Potential supervisors:
Project: Quantum orthogonal Latin squares?
Supervisors: Alexander Müller-Hermes and Geir Dahl
A mathematical result suggested by Euler in the 18th century and first proved in the 19th century says that there is no pair of orthogonal Latin squares of order 6. Another 100 years later, mathematicians and physicists studying quantum entanglement suggested a quantum variant of the problem: Here, a pair of orthogonal quantum Latin squares corresponds to a particular unitary operator acting on a tensor product of finite vector spaces. Surprisingly, it was proved very recently that there exist quantum orthogonal Latin squares of order 6. Besides this being a nice puzzle, there are many applications of quantum orthogonal Latin squares in the theory of entanglement and to design quantum error correcting codes for quantum computation. The goal of the project is to understand these fascinating results and to learn about their connections to other parts of quantum information science.
Prerequisite knowledge:
MAT1120 – Linear Algebra ?/?MAT1125 – Advanced linear algebra MAT2400 – Real Analysis MAT3400 – Linear Analysis with Applications MAT4430 – Quantum information theory
Project: Distances on the set of quantum channels
Supervisors Erik Bédos, Nadia S. Larsen and Tron Omland
Quantum channels are mathematically formulated as certain maps that transform the state of a quantum system into the state of another quantum system. There are well-understood descriptions of the possible form of a quantum channel in terms of some more basic building blocks. For quantum information processing it is desirable to monitor and control the changes imposed on quantum states arising from deviations in quantum channels when the systems undergo some time evolution. This requires having good notions of a distance on the set of quantum channels. The project will look at one or several notions of distance on the set of quantum channels with focus on particular classes of channels where one can carry out explicit computations.
Prerequisite knowledge:
MAT1120 – Linear Algebra ?/?MAT1125 – Advanced linear algebra MAT2400 – Real Analysis MAT3400 – Linear Analysis with Applications MAT4430 – Quantum information theory
Quantum mathematics and operator algebras
Potential supervisors:
Project: Braid groups and topological quantum field theory?
Supervisor: Makoto Yamashita
This master project is about the relation between the representation of type B braid groups and associated tensor categorical structures. The relation between type A braid groups, braided categories, and quantum field theories was an important guiding principle that led to many developments in mathematics and theoretical physics in the last 30 years. The type B braid group, which is given by the usual type A braid group and an extra generator, corresponds to the quantum field theories with boundary, and the braided module categories. Our goal is to find new examples of braided module categories (or equivalent structures such as algebra objects with ribbon braid), and to understand the induced representations of type B braid groups. We will also look at the problem of universality, that is, whether the images of these representations are dense in the projective model of the intertwiner spaces. This is expected to have application to quantum computation.
Prerequisite knowledge:
Project: Matrix convexity and entropy
Supervisor: Makoto Yamashita
This project is about operator monotonicity and operator convexity. These are related to important operations around mathematical physics modeled in the framework of operators on Hilbert spaces. A class of real functions f(x) called *operator monotone functions* exhibit strong convexity properties. This can be used to prove important convexity / concavity relations for von Neumann entropy and its variants. We plan to look at the theory of quantum f-divergence developed by Hiai, and improve known results (mostly about functions f(x) = x^p) to general operator monotone functions.
Prerequisite knowledge:
MAT1120 – Linear Algebra ?/?MAT1125 – Advanced linear algebra MAT2400 – Real Analysis MAT3400 – Linear Analysis with Applications
Project: Mathematical framework of the bulk-edge correspondence?
Supervisor: Sergey Neshveyev
The bulk-edge correspondence is a general principle that says that properties of the interior (bulk) of a matter are reflected in properties of the boundary (edge). Such properties can be very different, a famous example being topological insulators, where the interior behaves as an electrical insulator while its surface is an electrical conductor. There have been suggested several mathematical frameworks aiming to rigorously describe such phenomena. The goal of the project would be to explore one, or possibly some, of them, depending on the background and interests of the student.
Prerequisite knowledge:
MAT1120 – Linear Algebra ?/?MAT1125 – Advanced linear algebra MAT2400 – Real Analysis MAT3400 – Linear Analysis with Applications
Project: Dynamical Lie algebras of quantum circuits?
Supervisors: Franz Fuchs and Makoto Yamashita
The dynamics of a quantum system is generated by Hamiltonians whose exponentials produce unitary time evolution. When multiple Hamiltonians are available, the commutators of these generators produce a Lie algebra known as the dynamical Lie algebra of the system. This algebra determines the set of reachable quantum operations and therefore characterizes the controllability and expressive power of quantum circuits. Dynamical Lie algebras play an important role in quantum control, Hamiltonian simulation, and the theoretical analysis of variational quantum algorithms. In this master project, you will study the dynamical Lie algebras generated by families of Hamiltonians relevant to quantum computing. The project may involve computing Lie closures of sets of operators, analyzing the structure and dimension of the resulting Lie algebras.
Prerequisite knowledge:
Recommended knowledge:
FYS4110 – Advanced Quantum Mechanics MAT4270 – Representation Theory MAT-INF4130 – Numerical Linear Algebra (discontinued)
Computational mathematics
Potential supervisors:
Project: Numerical methods for Fokker–Planck equations arising from underdamped Langevin dynamics?
Supervisor H?kon Hoel
This project develops new numerical methods for kinetic Fokker–Planck equations arising from underdamped Langevin dynamics, central in statistical mechanics and molecular dynamics. Instead of solving directly for the probability density, it uses a recent “Schr?dingerisation” framework: the problem is embedded into a larger Schr?dinger-type system for a wave function, and the physical density is recovered as a quadratic marginal. This preserves key structural properties (positivity, conservation, equilibrium) and allows the use of efficient numerical schemes for Schr?dinger equations.
Prerequisite knowledge:
FYS3110 – Quantum Mechanics MAT3360 – Introduction to Partial Differential Equations MAT4301 – Partial Differential Equations
Project: Cartan decompositions of unitary groups and quantum circuit synthesis?
Supervisors: Franz Fuchs and Makoto Yamashita
Quantum computing relies on the implementation of unitary transformations on multi-qubit systems. In practice, these transformations must be decomposed into sequences of elementary quantum gates that can be executed on hardware. A powerful mathematical framework for such decompositions is the Cartan (or KAK) decomposition of Lie groups. For example, any two-qubit unitary operation can be expressed as a sequence of local operations acting on individual qubits and a canonical non-local operation determined by the Cartan subalgebra of SU(4). In this project, you will study Cartan decompositions of unitary groups and their applications to quantum circuit synthesis. The work may combine analytical techniques from Lie theory with computational tools for symbolic algebra and numerical simulation.
Prerequisite knowledge:
Recommended knowledge:
FYS4110 – Advanced Quantum Mechanics MAT4270 – Representation Theory MAT-INF4130 – Numerical Linear Algebra (discontinued)
Department of Chemistry
Quantum materials
Project X: Topological systems in complex oxide thin films grown by atomic layer deposition
Supervisor: Assoc. Prof. Henrik H. S?nsteby
Project description:
In this type of master project, you will study topological phases and emergent quantum phenomena in complex oxide thin films synthesized using atomic layer deposition (ALD). Complex oxides provide a versatile platform for realizing topological states due to the interplay between strong electron correlations, spin–orbit coupling, lattice distortions, and interface effects. Relevant projects include growth and optimization of oxide heterostructures, exploration of candidate topological oxide systems, and investigation of how structural parameters, stoichiometry, and interfaces influence electronic and topological properties. These materials are of interest for applications in low-dissipation electronics and future quantum technologies.
Methodology for master project:
Thin-film growth using atomic layer deposition (ALD), combined with structural, electronic, and transport characterization (e.g., X-ray diffraction, atomic force microscopy, electrical transport measurements).
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project Y: Design and synthesis of solid quantum materials
Supervisor: Prof. Martin Valldor
Project description: During this master project you will work experimentally to synthesize (chemically) and characterize (x-ray diffraction and further advanced techniques) solid-state crystalline compounds that belong to quantum materials. These materials can be one of the following: frustrated magnets, spintronics, multiferroics, single-ion-molecular magnets, or superconductors. These material groups can deliver usable technology for future data storage (qubits), signaling (by single particle), and quantum entanglements (the basic principle for quantum computing). Each discovery will bring further understanding towards the interplay between charge-spin-orbital-lattice, which is most fundamental for quantum materials.
Methodology for master project: Inorganic chemistry, diffraction, electron microscopy, elemental analysis, magnetism, conductivity, phase transitions.
Prerequisite knowledge:
MENA3001 – Functional Materials - Enten?
KJM3121 – Inorganic Materials Chemistry ?eller?MENA3120 MENA3100 – Characterization of Materials KJM2500 – Synthesis and Characterisation
Recommended courses to take during first semesters of master programme:
Computational quantum chemistry
In computational quantum chemistry, the laws of physics are applied to chemical systems in gas and condensed phases, including the solid state. Electrons are described as many-particle quantum systems, while the nuclei may be treated as either quantum or classical particles, depending on the processes, phenomena, and type of system under study. A wide range of computational methodologies have been developed to address the challenge of rapidly increasing computational complexity as the number of particles is increased. This includes sophisticated quantum-mechanical models for electrons and nuclei, machine-learned potentials for molecular dynamics, and generative AI models for molecular and materials discovery. A master project in computational quantum chemistry involves development and/or application of such methodologies to study quantum phenomena with potential applications to quantum technologies.
Project CQC1: Quantum control
Supervisors: Prof. Thomas Bondo Pedersen, Ass. prof. Simen Kvaal
Quantum control is a grand challenge for quantum science and technology. It entails the application of forces to steer a quantum system from a given initial state to a final state with desired properties. Examples include controlling open quantum systems such as material defects and chemical processes through the entanglement of electronic and nuclear degrees of freedom induced by ultrashort (atto- and few-femtosecond) laser pulses. The accurate simulation of such processes remains highly challenging. Solving the time-dependent Schr?dinger equation encompasses a broad range of methodologies: from single-particle wavefunctions represented on grids or via adaptive basis functions, through time integration of stiff ordinary differential equations while preserving physical invariants, software development and high-performance computing, 3D visualization, and the development and application of machine-learning models to determine optimal laser-pulse parameters. The exact formulation of the project will depend on the student’s interests.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
FYS4110 – Advanced Quantum Mechanics FYS4480 – Quantum mechanics for many-particle systems KJM5631 – Multi-Scale Molecular Modeling
Project CQC2: Quantum chemistry on NISQ devices
Supervisors: Ass. prof. Simen Kvaal, Prof. Thomas Bondo Pedersen
Project description: For noisy intermediate-scale quantum (NISQ) devices, unitary coupled-cluster (UCC) theory, with applications to the electronic Schr?dinger equation, is considered one of the most promising application areas. Possible master projects include the study of UCC and its variants, simulation of UCC-based calculations, development of new approaches, and investigation of the effects of noise and error mitigation or correction.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
FYS4110 – Advanced Quantum Mechanics FYS4480 – Quantum mechanics for many-particle systems KJM5631 – Multi-Scale Molecular Modeling
Project CQC3: Development of DFT approaches
Supervisors: Erik Tellgren, Ass. prof. Simen Kvaal
Project description: DFT is routinely used for computational investigations of molecules and materials, including semiconductor defects for quantum sensing. Key challenges include the development and testing of more accurate density-functional approximations, as well as many-body models that go beyond standard DFT. Machine learning approaches and traditional analytical (“pen-and-paper”) development go hand in hand with software development, including advanced visualization approaches, in this area.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
FYS4110 – Advanced Quantum Mechanics FYS4480 – Quantum mechanics for many-particle systems KJM5631 – Multi-Scale Molecular Modeling
Project CQC4: Magnetic-field effects on chemical bonding and spectra
Supervisors: Erik Tellgren, Prof. Thomas Bondo Pedersen
Project description: In this master project, you will use quantum-chemical methods to study magnetic field effects on molecular systems and simple models of point defects. Depending on model parameters, this is of interest for astrophysical spectra from molecules in very strong magnetic fields, properties of materials in weaker magnetic fields that can be generated on Earth, or magnetic-field effects on free and laser-induced quantum dynamics.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
FYS4110 – Advanced Quantum Mechanics FYS4480 – Quantum mechanics for many-particle systems KJM5631 – Multi-Scale Molecular Modeling
Project CQC5: Inverse design of quantum materials with generative AI
Supervisor: David Balcells
Project description: In this master project, you will develop and apply physics-informed data, representations, and methods for inverse design models based on generative AI, enabling the property-conditioned generation of quantum systems. Development will focus on probabilistic variational autoencoders and diffusion models. Applications will focus on the inverse design and data-driven discovery of quantum materials (e.g., single-molecule quantum magnets).
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project CQC6: Predicting quantum properties with discriminative AI
Supervisor: David Balcells
Project description: In this master project, you will develop and apply discriminative AI models enabling the accurate and transferable prediction of quantum properties (e.g., energy gaps) and effects (e.g., spin-orbit coupling), as well as the ultra-fast screening of large combinatorial spaces. Synergies with genetic algorithms will be also investigated. Applications will focus on quantum control through the fine-tuning of quantum properties and effects having a strong influence on systems of broad interest, including catalysts and transition metal qubits.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project CQC7: Computational spectroscopy of molecular qubits
Supervisor: Abril Castro Aguilera
Project description: In this master’s project, you will use state-of-the-art quantum-chemistry methods to predict and interpret the structural, electronic, and spectroscopic properties of molecular qubits such as transition-metal complexes and lanthanide complexes relevant to quantum-technology applications. The work directly connects non-relativistic and relativistic quantum theory with experiments, focusing on interpreting challenging magnetic properties such as zero-field splitting, g-tensors, and hyperfine couplings, and on large magnetic anisotropy and strong spin-orbit coupling.
Prerequisite knowledge:
Recommended courses to take during first semesters of master programme:
Project CQC8: Machine learning for superconducting materials discovery
Supervisor: Sigbj?rn L?land Bore
Project Description: Predicting the critical temperature of a superconductor is a two-part challenge: determining how atoms vibrate (phonons) and how those vibrations scatter electrons (coupling). Traditionally, both are calculated using Density Functional Theory (DFT), which is computationally expensive for complex crystals or large supercells. In this project, you will develop a hybrid workflow using Machine Learning Interatomic Potentials (MLIPs) to handle the vibrational part of the problem. This allows for fast structural relaxation and efficient calculation of the phonon spectrum. You will then use DFT to calculate the electronic coupling. This workflow combines the speed of machine learning with the proven accuracy of quantum mechanical calculations. If time permits, the project can be extended to utilize Machine-Learned Hamiltonians (ML-Ham) to predict electronic eigenvalues and deformation potentials directly, potentially bypassing the explicit DFT coupling step.
Prerequisite Knowledge:
Recommended Courses to take during the master programme:
Department of Informatics
Hybrid quantum-classical programming
This project investigates the foundation of hybrid quantum-classical programming (HQP). Due to inherent limitations of quantum computers, addressing challenging real-world problems using quantum computers - now and in the future - will require a hybrid approach that combines massively parallel classical high-performance computing (HPC) on big data, with the delegation of classically intractable subproblems on relatively small data sets to quantum computers.
Projects in this topic can be angled towards different areas such as
- Quantum programming language design
- Tensor models
- Models for quantum algebras (ZX-calculus, etc.)
- High-level compilation and optimisation of quantum computations
Potential supervisors: