Quantum circuit complexity and unsupervised machine learning of topological order.

Area of Science:

• Quantum Physics
• Machine Learning
• Quantum Information Theory

Background:

• Discovering unknown quantum many-body phases is a significant challenge.
• Unsupervised machine learning offers potential solutions for complex quantum systems.

Purpose of the Study:

• To explore quantum circuit complexity as a tool for unsupervised machine learning in quantum physics.
• To develop intuitive and efficient methods for identifying topological order in quantum many-body systems.

Main Methods:

• Utilizing Nielsen's quantum circuit complexity as an intrinsic informational distance.
• Connecting quantum circuit complexity with quantum Fisher complexity (Bures distance) and entanglement generation through two theorems.
• Developing kernel functions based on these connections.

Main Results:

• Demonstrated superior performance and enhanced interpretability of the developed kernel functions in numerical multiqubit experiments.
• Established quantum circuit complexity as a viable metric for manifold learning of topological quantum states.

Conclusions:

• Quantum circuit complexity provides an interpretable framework for unsupervised machine learning of topological quantum order.
• The study bridges quantum computation, complexity, metrology, and machine learning.