Here, you can find a list of my publications and preprints. They are sorted in order of appearance on the arXiv (beginning with the latest)

**A critical lattice model for a Haagerup conformal field theory**

*Joint work with Robijn Vanhove, Laurens Lootens, Maarten Van Damme, Tobias Osborne, Jutho Haegeman, and Frank Verstraete*

ArXiv: 2110.03532

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category H3 as input data. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory (CFT) with central charge c=2. Generalized twisted CFT spectra are numerically obtained through exact diagonalization of the transfer matrix and the conformal towers are separated in the spectra through their identification with the topological sectors. It is further argued that our model can be obtained through an orbifold procedure from a larger lattice model with input Z(H3), which is the simplest modular tensor category that does not admit an algebraic construction. This provides a counterexample for the conjecture that all rational CFT can be constructed from standard methods.

**Computing associators of endomorphism fusion categories**

*Joint work with Daniel Barter and Jacob Bridgeman*

ArXiv: 2110.03644

Many applications of fusion categories, particularly in physics, require the associators or F-symbols to be known explicitly. Finding these matrices typically involves solving vast systems of coupled polynomial equations in large numbers of variables. In this work, we present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data. Given a module category over the latter, we utilize the representation theory of a module tube category, built from the known data, to compute this unknown associator data. When the input category is unitary, we discuss how to ensure the obtained data is also unitary.

We provide several worked examples to illustrate this algorithm. In addition, we include several Mathematica files showing how the algorithm can be used to compute the data for the Haagerup category H1, whose data was previously unknown.

**Device-independent quantum key distribution with random key basis**

*Joint work with René Schwonnek, Koon Tong Goh, Ignatius W. Primaatmaja, Ernest Y.-Z. Tan, Valerio Scarani, Charles C.-W. Lim*

ArXiv: 2005.02691

Journal: *Nature Communications* **12**, 2008 (2021)

Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today’s loophole-free Bell experiments. Here, we significantly narrow the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. By using two randomly chosen key generating bases instead of one, we show that our protocol significantly improves over the original DIQKD protocol, enabling positive keys in the high noise regime for the first time. We also compute the finite-key security of the protocol for general attacks, showing that approximately 10^{8}–10^{10} measurement rounds are needed to achieve positive rates using state-of-the-art experimental parameters. Our proposed DIQKD protocol thus represents a highly promising path towards the first realisation of DIQKD in practice.

**Generalized string-nets for unitary fusion categories without tetrahedral symmetry**

*Joint work with Alexander Hahn*

ArXiv: 2004.07045

Journal: Physical Review B 102, 115154 (2020)

The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. However, the original construction is not applicable to all unitary fusion category since some additional symmetries for the F-symbols are imposed. In particular, the so-called tetrahedral symmetry is not fulfilled by many interesting unitary fusion categories. In this paper, we present a generalized construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories that works without requiring these additional symmetries. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.

**Gauging defects in quantum spin systems: A case study**

*Joint work with Jacob C. Bridgeman, Alexander Hahn*, and Tobias J. Osborne

ArXiv: 1910.10619

Journal: Physical Review B 101, 134111 (2020)

The goal of this work is to build a dynamical theory of defects for quantum spin systems. This is done by explicitly giving an exhaustive case study of a one-dimensional spin chain with Vec(Z/2Z) fusion rules, which can easily be extended to more general settings. A kinematic theory for an indefinite number of defects is first introduced exploiting *distinguishable Fock space*. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the *golden chain*. Technically, this is done by employing generalized tube algebra techniques to model the defects in the chain. We illustrate this approach for the Vec(Z/2Z) spin chain, in whose case the resulting dynamical defect model is equivalent to the critical transverse Ising model.

**The F-Symbols for the H3 Fusion Category**

*Joint work with Tobias J. Osborne and Deniz E. Stiegemann*

ArXiv: 1906.01322

We present a solution for the F-symbols of the H3 fusion category, which is Morita equivalent to the even parts of the Haagerup subfactor. This solution has been computed by solving the pentagon equations and using several properties of trivalent categories.

**Training deep quantum neural networks**

*Joint work with *Kerstin Beer, Dmytro Bondarenko, Terry Farrelly, Tobias J. Osborne, Robert Salzmann, and Daniel Scheiermann

ArXiv: 1902.10445

Journal: Nature Communications 11, 808 (2020)

Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

This article is among the Top 50 Nature Communications physics articles published in 2020!

**From categories to anyons: a travelogue**

*Joint work with Kerstin Beer, Dmytro Bondarenko, Alexander Hahn, Maria Kalabakov, Nicole Knust, Laura Niermann, Tobias J. Osborne, Christin Schridde, Stefan Seckmeyer, Deniz E. Stiegemann*

ArXiv: 1811.06670

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the „highlights for a physicist“.

**Entanglement detection by violations of noisy uncertainty relations: A proof of principle**

*Joint work with Yuan-Yuan Zhao, Guo-Yong Xiang, Xiao-Min Hu, Bi-Heng Liu, Chuan-Feng Li, Guang-Can Guo, René Schwonnek*

ArXiv: 1810.05588

Journal: Physical Review Letters 122, 220401 (2019)

It is well known that the violation of a local uncertainty relation can be used as an indicator for the presence of entanglement. Unfortunately, the practical use of these nonlinear witnesses has been limited to few special cases in the past. However, new methods for computing uncertainty bounds have become available. Here we report on an experimental implementation of uncertainty-based entanglement witnesses, benchmarked in a regime dominated by strong local noise. We combine the new computational method with a local noise tomography in order to design noise-adapted entanglement witnesses. This proof-of-principle experiment shows that quantum noise can be successfully handled by a fully quantum model in order to enhance the ability to detect entanglement.