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

One of the earliest conceived advantages quantum computers have over classical computers is in simulating the dynamics of closed quantum systems. In comparison, the problem of ground state computation is harder for it to solve, especially in the case of strongly correlated systems. Here, we devise a method to study the microcanonical phase diagram of strongly correlated quantum systems from dynamics data. We introduce a concept called time-averaged classical shadows (TACS), which borrows from the quantum tomography method called classical shadows, as well as Von Neumann's idea of the time-averaged density matrix, to construct thermal state representations from dynamics data. We simulate microcanonical quantum dynamics for the 1D transverse field Ising model to generate TACS data, then deploy an unsupervised machine learning method called diffusion maps to learn the phases. Our results show that machine learning methods can learn quantum phase transitions from TACS data, suggesting quantum computers will be capable of mapping out microcanonical phase diagrams in the near term.

Second of two, this talk will focus on the machine learning methods and the results of our work.