Topological phases of matter have emerged as a new branch within condensed matter physics as they cannot be described using Landau’s traditional classification of phases using local order parameters. These phases are particularly intriguing for applications involving quantum information storage and processing due to the presence of protected edge modes and robustness against local perturbations.
Our research investigates the class of symmetry-protected topological (SPT) models on spin or fermion lattices, where non-trivial topology arises from the underlying symmetries. Specifically, we are interested in the behaviour of these models when coupled to an environment, thereby accounting for dissipation. By incorporating dissipation into our models, we enhance the correspondence between theoretical predictions and experimental imperfections giving valuable insights that can inform hardware design.
To mathematically describe the time evolution, we employ the Lindblad master equation which provides a description of the averaged dynamics. Alternatively, we can explore the stochastic dynamics using quantum trajectories which carries more information since it retains information on each individual path in state space. While taking an ensemble average reduces this method to the Lindbladian approach, analysing individual stochastic realisations offers deeper insights and more intuitive physical interpretation of the exact path that the system takes through state space.
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