Main research directions

Both quantum and classical computing is inherently based on nonequilibrium coherent dynamics of quantum systems. Thermalization and dephasing are considered to be parasitic effects erasing the information about the quantum state both in quantum and classical computing. Thus it is a subject of intensive theoretical and experimental studies to get rid of such effects. Up to now there exist two major distinct methods to preserve the initial state information.

First one, the topological protection of the desired states, is actively used for fault-tolerant quantum computations and is associated to braiding protocols of Majorana modes. Despite quite a number of theoretical and experimental work and Majorana mode observation, there are significant limitations preventing the realization of their braiding and its relevant theoretical description. The main difficulty is to include the interaction preserving a particle parity into the above picture. In the research direction "Quantum dynamics of superconducting topological systems" we develop the methods for a quantum mechanical description of a Majorana nanowire subject to the interactions (such as Coulomb blockade). This will allow us to find fundamental limitations and possible bypasses for Majorana mode braiding and be highly desirable by fault quantum computation community.

Second method is to apply quenched disorder to a system forcing it to undergo a many-body localization (MBL) transition, completely preventing thermalization. The hardest task here is the analytical description of MBL, and it is of particular concern and high demand to model essential attributes of such systems in less complicated single-particle and random matrix models.
Even at smaller disorder values below MBL interacting systems might show non-thermalizing behavior characterized by multifractal states. Such states provide a unique opportunity for speeding-up quantum annealing or parallel tempering. Multifractal states are also useful for swift and accurate sampling of rare local minima in the Hilbert space crucially needed for efficient training in machine learning. In this part called "Non-ergodic phases of matter" the main purposes are to suggest and investigate disordered models with the robust non-ergodic phases of matter for their application to machine learning, quantum annealing, and quantum memory. In the related direction "Relations between entanglement and multifractality" we consider the role of entanglement and multifractality in quantum dynamics and thermalization of many-body disordered systems in MBL and thermalizing parameter range.

In the last, but not the least direction "Interplay of correlations and localization in long-range disordered systems" the main focus is on the localization effects in various long-range models (e.g., dipolar ones) which are relevant as for the experimental realizations in trapped ions and ultracold atoms as for the transistors in state-of-art computers. The latter are already close to the limit of the fully quantum transport and therefore are subjected to the disorder effects localizing electrons in thin films and narrow wires at any impurity concentration. Only due to electron-photon and electron-phonon scattering charges can still propagate at long-range distances in such wires and overcome localization effects. However, the correlations, anisotropy and time-reversal symmetry in long-range electron hopping crucially affect localization properties and may even localize almost all states in the system. This is the main topic of the above direction.