Quantum Circuit Complexity Enhances Machine Learning for Topological Order
Researchers have explored the use of quantum circuit complexity as a tool for unsupervised machine learning to discover unknown quantum many-body phases of matter. This approach leverages Nielsen's quantum circuit complexity to serve as an intrinsic informational distance between topological quantum states, facilitating interpretable manifold learning. The study presents two theorems connecting quantum circuit complexity with quantum Fisher complexity and entanglement generation, demonstrating superior performance in numerical multiqubit experiments. This research establishes connections between quantum computation, complexity, metrology, and machine learning of topological quantum order. 
