Revealing microcanonical phase diagrams of strongly correlated systems via time-averaged classical shadows

• URL: http://arxiv.org/abs/2211.01259v2
• Date: Tue, 20 Dec 2022 02:41:06 GMT
• Title: Revealing microcanonical phase diagrams of strongly correlated systems via time-averaged classical shadows
• Authors: Gaurav Gyawali, Mabrur Ahmed, Eric Aspling, Luke Ellert-Beck, Michael J. Lawler
• Abstract summary: We propose a method to study microcanonical phases and phase transitions on a quantum computer from quantum dynamics. We first show that this method, applied to ground state calculations on 100 qubit systems, discovers the geometric relationship between magnetization and field. We then show that diffusion maps of TACS data from quantum dynamics simulations efficiently learn the phase-defining features and correctly identify the quantum critical region.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 microcanonical phases and phase transitions on a quantum computer from quantum dynamics, by introducing time-averaged classical shadows (TACS) of the von Neumann ensemble, the time average of the density matrix, and combining it with machine learning via diffusion maps. Using the one-dimensional transverse field Ising model(1DTFIM), and a kernel function developed for classical shadows, we first show that this method, applied to ground state calculations on 100 qubit systems, discovers the geometric relationship between magnetization and field. We then show that diffusion maps of TACS data from quantum dynamics simulations efficiently learn the phase-defining features and correctly identify the quantum critical region. The machine-learned features include an observable that exhibits a singularity at the quantum critical point and entropy, the primary thermodynamic potential of the microcanonical ensemble. To verify this, we fit these features to susceptibility, computed directly using TACS, and the second Renyi entropy estimated using a Bayesian inference model. Our results provide evidence that quantum simulators and computers capable of outperforming classical computers at dynamics simulations may also produce quantum thermodynamic data with quantum advantage.

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