Recently, there has been substantial progress in methods of identifying local integrals of motion in interacting integrable models or in systems with many-body localization. We show that one of these approaches can be utilized for constructing local, conserved, Majorana fermions in systems with an arbitrary many-body interaction. As a test case, we first investigate a non-interacting Kitaev model and demonstrate that this approach perfectly reproduces the standard results. Then, we discuss how the many-body interactions influence the spatial structure and the lifetime of the Majorana modes. Finally, we determine the regime for which the information stored in the Majorana correlators is also retained for arbitrarily long times at high temperatures. We show that it is included in the regime with topologically protected soft Majorana modes, but in some cases is significantly smaller.

We are at the verge of a new era, which will be dominated by Noisy Intermediate-Scale Quantum Devices. Prototypical examples for these new technologies are present-day quantum annealers. In the present work, we investigate to what extent static disorder generated by an external source of noise does not have to be detrimental, but can actually assist quantum annealers in achieving better performance. In particular, we analyze the graph coloring problem that can be solved on a sparse topology (i.e. chimera graph) via suitable embedding. We show that specifically tailored disorder can enhance the fidelity of the annealing process and thus increase the overall performance of the annealer.

Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. in particular, quantum annealers. there exist a plethora of algorithms promising to outperform classical computers in the near-term future. Here, we propose a parallel in time approach to simulate dynamical systems designed to be executed already on present-day quantum annealers. in essence, purely classical methods for solving dynamics systems are serial. therefore, their parallelization is substantially limited. in the presented approach, however, the time evolution is rephrased as a ground-state search of a classical ising model. Such a problem is solved intrinsically in parallel by quantum computers. The main idea is exemplified by simulating the Rabi oscillations generated by a two-level quantum system (i.e. qubit) experimentally.