Unsupervised Learning of Non-Hermitian Topological Phases

Abstract

Non-Hermitian topological phases bear a number of exotic properties, such as the non-Hermitian skin effect and the breakdown of conventional bulk-boundary correspondence. In this paper, we introduce an unsupervised machine learning approach to classify non-Hermitian topological phases based on diffusion maps, which are widely used in manifold learning. We find that the non-Hermitian skin effect will pose a notable obstacle, rendering the straightforward extension of unsupervised learning approaches to topological phases for Hermitian systems ineffective in clustering non-Hermitian topological phases. Through theoretical analysis and numerical simulations of two prototypical models, we show that this difficulty can be circumvented by choosing the on-site elements of the projective matrix as the input data. Our results provide a valuable guidance for future studies on learning non-Hermitian topological phases in an unsupervised fashion, both in theory and experiment.

7+12 pages, 3+8 figures

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• Non-Hermitian skin effect beyond the tight-binding models
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Machine Learning of Knot Topology in Non-Hermitian Band Braids
• Experimental demonstration of adversarial examples in learning topological phases
• Unsupervised identification of Floquet topological phase boundaries
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• A simple framework for contrastive learning phases of matter
• Quaternion-based machine learning on topological quantum systems
• Topological analysis of the complex SSH model using the quantum geometric tensor
• Unsupervised Detection of Topological Phase Transitions with a Quantum Reservoir
• Quantum circuit complexity and unsupervised machine learning of topological order
• Classifying topological neural network quantum states via diffusion maps
• Manifold formation and crossings of ultracold lattice spinor atoms in the intermediate interaction regime
• Machine learning topological energy braiding of non-Bloch bands
• Anti-parity-time topologically undefined state
• Noise-Resilient Quantum Reinforcement Learning