Revealing microcanonical phase diagrams of strongly correlated electrons on quantum computers I

Quantum computers and simulators are promising platforms to simulate the dynamics of quantum many-body systems. Inspired by von Neumann’s time-averaged density matrix and recently developed classical shadow tomography technique, we introduce an approach called time averaged classical shadows(TACS) to study the quantum thermodynamic properties. We show that TACS can be used as an effective representation for unsupervised machine learning methods such as diffusion map to identify the microcanonical phases of strongly interacting electrons. Our results demonstrate that machine learning methods can identify quantum phase transitions from simulated microcanonical dynamics data suggesting quantum computers will be capable of mapping out microcanonical phase diagrams in the near term. In part I of this talk, we will discuss the theoretical underpinnings of our work.