Non-Equilibrium Manifold Distance for Open Quantum Systems

Fang et al. (2024) introduced manifold distance as a universal metric for topological phase transitions using fidelity and trace distance, but acknowledged limitations for non-lattice or open systems. This research would generalize their approach to Lindblad master equations, incorporating dissipative dynamics into the manifold distance calculation. Unlike their ground-state-focused method, we'd track steady-state density matrices under decoherence, revealing how topological invariants evolve when coupled to environments. This bridges the gap between their equilibrium framework and Chen & Grover's (2024) work on mixed-state topological transitions, potentially identifying new universality classes in non-Hermitian settings. The innovation lies in adapting quantum information metrics to noisy platforms like superconducting circuits (as in Xue & Hu 2021), enabling experimental validation of topological robustness against realistic imperfections.

References:

1. Distance between two manifolds, topological phase transitions and scaling laws. ZhaoXiang Fang, Ming Gong, Guangcan Guo, Yongxu Fu, Long Xiong (2024).
2. Unconventional topological mixed-state transition and critical phase induced by self-dual coherent errors. Yu-Hsueh Chen, Tarun Grover (2024). Physical review B.
3. Topological Photonics on Superconducting Quantum Circuits with Parametric Couplings. Z. Xue, Yong Hu (2021). Advanced Quantum Technologies.