Maximilian Balthasar Mansky, M. Sc.
Lehrstuhl für Mobile und Verteilte Systeme
Ludwig-Maximilians-Universität München, Institut für Informatik
Telefon: +49 89 / 2180-9155
Mobile: +49 179 5391026
Fax: +49 89 / 2180-9148
- Theoretical foundations of quantum computing
- Mathematical structures of QC
- Circuit length optimizations
- Near-optimal circuit construction via Cartan decomposition (in submission, arXiv:2212.12934)
- Dense neural networks induce connected submanifolds (in submission)
If you are interested in a topic that aligns with my own research interests, please reach out to me. You can also pick a topic from the list below:
Efficient universal gate sets for SU(4) and higher dimensions: Based on the work of Harrow et al, „Efficient discrete approximations of quantum gates“, extend their ideas to higher dimensions. You don’t need a strong math background for this thesis.
- Black-Scholes on Quantum. It is fairly well known that there is a direct correspondence between the Black-Scholes equation (modeling of prices of Options on stocks) and physical models, for example for Heat transfer. Less well known is the fact that the underlying differential equation is the same as the Schrödinger equation, just without the imaginary factor. Can this fact be used to map Black-Scholes/Heat models to a quantum computer? Some prior exposure to Black-Scholes/Heat model (Green’s equation) is beneficial, you should be comfortable with differential equations beyond a conceptual level.
- Topology of quantum machine learning. There is a fundamental difference between classical machine learning on ℝⁿ and its counterpart quantum ML on SU(2ⁿ). Beyond the larger state space, all curves (enclosing areas of classification) are closed – And stay closed when moving backwards through the layers of the neural network. In contrast, in classical machine learning open stays open. In this thesis, the difference and consequences thereof are to be examined. You should be at least be interested in the area of topology (Key words: push-forward; pull-back, Homomorphisms) and be somewhat with how machine learning works conceptually.
- Differences in data for quantum embedding. A recent paper (https://arxiv.org/abs/2303.01461) has shown that quantum symmetries and classical data can interact in subtle ways that make it easier or harder to embed the data on a quantum computer. In this thesis, you will understand this relationship in more detail and develop methods for detecting necessary symmetries in the classical data. Some understanding of the physics is helpful (Ising model in different arrangements).
- Intransitive states. The property transitivity means that if A> B and B>C, then A > C. Intransitive dice are an example where this property is not present in a stochastic context. Is it possible to construct an analogue for quantum experiments? Since this is a very open question, it is probably best suited for an Einzelpraktikum.