On the control of quantum many-body systems

Abstract

The ability to control and actively manipulate physical systems at a scale at which quantum properties manifest themselves is crucial for the development of quantum technologies. While, at present, it is possible to manufacture small-scale quantum devices, controlling quantum systems that consist of many degrees of freedom remains a formidable task. In this thesis, we look at the problem of stability and control of quantum information in complex quantum many-body systems. We explore two key aspects of this. The first deals with the manipulation of the information encoded in the degenerate ground- state manifold of systems possessing topological quantum order (TQO). In particular, we exploit Differentiable Programming (∂P) and Natural Evolution Strategies (NES) for the optimal transport of Majorana zero modes in topological p-wave superconductors. These machine learning techniques uncover novel optimal control strategies for Majoranas that are robust with respect to disorder or interactions. Furthermore, we show, using TQO, that topological quantum memories are protected from dynamically generated phase errors caused by small, interaction-driven, energy mismatches between bulk modes. This, in turn, can be used to derive constraints on the bulk energy spectrum of a complex many-body system. The second aspect concerns the problem of state transfer through a disordered many-body spin chain. We show that ∂P can be efficiently combined with the other quantum control techniques CRAB and shortcuts to adiabaticity. With this hybrid approach, we are able to improve the speed limit for the optimal transport of magnons in a clean Heisenberg model. In addition, in a disordered chain, perfect fidelity transport protocols can be obtained that are robust against fixed, unwanted, realizations of the noise. The fact that this setup can be implemented in a wide range of experimental platforms, makes our results relevant to real- world quantum-state transfer applications.