Identifying topological quantum phases in spin models with time-averaged classical shadows and unsupervised learning

Shadow tomography techniques such as classical shadows allow the discovery of quantum phases via Machine Learning algorithms by serving as a low-cost representation of a quantum state prepared on a quantum processor. Simultaneously, the time-averaged density matrix—representing the von Neumann ensemble—offers a computationally inexpensive way to study quantum phases via quantum dynamics. Building on these concepts, we have introduced Time-Averaged Classical Shadows (TACS), the classical shadows of the time-averaged density matrix. In this talk, I will discuss how we used TACS to characterize two paradigmatic models with topological phases—the cluster state model and the Toric Code model—employing and comparing multiple unsupervised machine learning techniques for phase classification. I will explore potential applications of our methods for achieving quantum advantage in simulating and classifying quantum phases via quantum dynamics and machine learning.