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The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications to quantum phase transitions. We use a recently proposed variational algorithm. The systems studied are the transverse Ising model with both a purely real and a purely complex transverse field., Comment: Proceedings for LFT conference poster, 10 pages, 3 figures

We study the optimal placement of wind turbines within a windfarm to maximize the power produced by mapping the system to a Quadratic Unconstrained Binary Optimisation (QUBO) problem. We investigate solving the resulting QUBO problem using the Variational Quantum Eigensolver (VQE) on a quantum computer simulator and compare the results to those from two classical optimisation methods: simulated annealing and the Gurobi solver. The maximum grid size we study is 4 $\times$ 4, which requires 16 qubits., Comment: Fixed several typos throughout the text. Added a few extra references to Section 7.5

In previous work, we developed a single Evolutionary Algorithm (EA) to solve random instances of the Anshel-Anshel-Goldfeld (AAG) key exchange protocol over polycyclic groups. The EA consisted of six simple heuristics which manipulated strings. The present work extends this by exploring the use of hyper-heuristics in group-theoretic cryptology for the first time. Hyper-heuristics are a way to generate new algorithms from existing algorithm components (in this case the simple heuristics), with the EAs being one example of the type of algorithm which can be generated by our hyper-heuristic framework. We take as a starting point the above EA and allow hyper-heuristics to build on it by making small tweaks to it. This adaptation is through a process of taking the EA and injecting chains of heuristics built from the simple heuristics. We demonstrate we can create novel heuristic chains, which when placed in the EA create algorithms which out-perform the existing EA. The new algorithms solve a markedly greater number of random AAG instances than the EA for harder instances. This suggests the approach could be applied to many of the same kinds of problems, providing a framework for the solution of cryptology problems over groups. The contribution of this paper is thus a framework to automatically build algorithms to attack cryptology problems., Comment: 16 pages

We have performed a detailed study of the lattice distortions of InP wurtzite nanowires containing an axial screw dislocation. Eshelby predicted that this kind of system should show a crystal rotation due to the dislocation induced torque. We have measured the twisting rate and the dislocation Burgers vector on individual wires, revealing that nanowires with a 10-nm radius have a twist up to 100% larger than estimated from elasticity theory. The strain induced by the deformation has a Mexican-hat-like geometry, which may create a tube-like potential well for carriers., Comment: 5 pages, 3 figues

Nanometric inclusions filled with nitrogen, located adjacent to FenN (n = 3 or 4) nanocrystals within (Ga,Fe)N layers, are identified and characterized using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). High-resolution STEM images reveal a truncation of the Fe-N nanocrystals at their boundaries with the nitrogen-containing inclusion. A controlled electron beam hole drilling experiment is used to release nitrogen gas from an inclusion in situ in the electron microscope. The density of nitrogen in an individual inclusion is measured to be 1.4 +- 0.3 g/cm3. These observations provide an explanation for the location of surplus nitrogen in the (Ga,Fe)N layers, which is liberated by the nucleation of FenN (n> 1) nanocrystals during growth.

The energy-loss near-edge structure (ELNES) at the oxygen $K$ edge in two $AB_2O_4$ spinels (A=Mg, B=Al,Cr) is reported. In $MgAl_2O_4$ the experimental data is successfully modelled within the LDA framework. In the case of $MgCr_2O_4$ spin-polarisation, in the form of antiferromagnetic ordering on the Cr sub-lattice, must be included despite the fact that the measurements were performed at approximately 30 times above $T_N$. A model in which dynamic short-range antiferromagnetic ordering is present at room temperature is proposed to explain the results of the experiments and calculations., Comment: 10 pages, 3 figures