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Lecture notes in computer science

Efficient Dynamical Simulation of Strongly Correlated One-Dimensional Quantum Systems

Stephen R. L. Clark, Dieter Jaksch

Published Jan 1, 2006• 1 citation
Publisher
DOI
10.1007/11666806_63

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We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one- and two-dimensional many-body localization systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the time dynamics of quantum many-body systems in classical or artificial neural networks.
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 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.
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.