One way to understand states in quantum mechanics is by classifying them in terms of their entanglement structure. This is however an immensely difficult problem, and so one can restrict to analyzing so-called invariants---if two states have different variants, they are necessarily different. This research topic is on understanding these invariants for stabilizer states (and codes!), and what they can tell us about what can be done with them.

For related research, see here.

A great deal of effort is put into simulating noisy quantum systems. One thing that complicates this is the stochastic nature of some operations; some processes might fail and will have to restart, making it hard(er) to sample the relevant data from such simulations. One can get around this by characterizing certain properties, such as the average time until completion, or the average noise. More practical would be even a characterization of the underlying probability distributions. This knowledge could be used to speed up simulations, or, in some cases, make them unnecessary. Here, I am interested in using analytics wherever possible, but also in numerics obtained through tools such as tensor networks.

The theory of distillation and distribution of bipartite entanglement is at this point relatively well-understood, at least in certain idealized settings. This is not the case for multipartite entanglement, not even for certain idealized settings. Distributing stabilizer states is closely related to the so-called vertex-minor problem in graph theory. Even though the general case is hard, I am predominantly interested in using the underlying theory to find heuristic approaches for practical settings.

For distillation, I am interested in what happens when one is given a random assortment of noisy stabilizer states, distributed over the parties. In such a setting, it is not even clear how one would describe mathematically the allowed transformations on the states, let alone optimize over them.

In practice entanglement is always imperfect; there's noise that prevents it from being as useful as it could be. Somewhat surprisingly, it is possible to concentrate the entanglement present in a larger number of very noisy states, into a smaller number of less noisy states. One thus effectively distills the entanglement.

My colleagues and I have worked on understanding the different protocols one could perform to distill entanglement. We found a mathematical connection between such protocols and graphs. Exploiting this connection allowed us to find optimal protocols, and heuristics on how to best implement them with noisy circuitry.

Near-term n to k distillation protocols using graph codes

Enumerating all bilocal Clifford distillation protocols through symmetry reduction

Distributing bipartite entanglement is a basic primitive for the quantum internet. A significant amount of research has been poured into understanding how well this can be done with current and near-term .  Quite often, a fixed protocol is assumed, which may lead to sub-optimal performance. This is undesirable, especially with the limitations of near-term quantum technologies in mind.

For this project, we came up with a heuristic method for optimizing repeater schemes for inhomogeneous repeater chains. Our method is general, allowing us to apply it to two different type of implementations. This allowed us not only to understand what can be done with near-term quantum communication technologies, but also how this should be done, by outlining certain heuristics.

Optimizing repeater schemes for the quantum internet