Revealing microcanonical phases and phase transitions of strongly correlated electrons via time-averaged classical shadows

TL;DR

This paper introduces a method using time-averaged classical shadows to analyze quantum thermodynamics and phase transitions in strongly correlated electrons, enabling efficient phase diagram learning from limited quantum data.

Contribution

It proposes the concept of time-averaged classical shadows and demonstrates their effectiveness in learning phase diagrams from quantum dynamics data.

Findings

Successfully learned phase diagrams of the transverse field Ising model.

Demonstrated quantum advantage with fewer shots in quantum thermodynamic data.

Applied machine learning to quantum state trajectories for phase transition detection.

Abstract

Quantum computers and simulators promise to enable the study of strongly correlated quantum systems. Yet, surprisingly, it is hard for them to compute ground states. They can, however, efficiently compute the dynamics of closed quantum systems. We propose a method to study the quantum thermodynamics of strongly correlated electrons from quantum dynamics. We define time-averaged classical shadows (TACS) and prove it is a classical shadow(CS) of the von Neumann ensemble, the time-averaged density matrix. We then show that the diffusion maps, an unsupervised machine learning algorithm, can efficiently learn the phase diagram and phase transition of the one-dimensional transverse field Ising model both for ground states using CS \emph{and state trajectories} using TACS. It does so from state trajectories by learning features that appear to be susceptibility and entropy from a total of 90,000 shots taken along a path in the microcanonical phase diagram. Our results suggest a low number of shots from quantum simulators can produce quantum thermodynamic data with a quantum advantage.