[Paper Review] Measuring quantum entanglement, machine learning and wave function tomography: Bridging theory and experiment with the quantum gas microscope

Norm M. Tubman|arXiv (Cornell University)|Sep 26, 2016

Quantum many-body systems3 citations

TL;DR

This paper proposes a framework for exact wave function tomography in quantum gas microscopes, enabling direct measurement of quantum entanglement in interacting bosonic systems—previously thought infeasible—by replacing variational Monte Carlo sampling with experimental snapshots. The method leverages real-space data to optimize variational wave functions, bridging theory and experiment for large quantum systems.

ABSTRACT

There is an enormous amount of information that can be extracted from the data of a quantum gas microscope that has yet to be fully explored. The quantum gas microscope has been used to directly measure magnetic order, dynamic correlations, Pauli blocking, and many other physical phenomena in several recent groundbreaking experiments. However, the analysis of the data from a quantum gas microscope can be pushed much further, and when used in conjunction with theoretical constructs it is possible to measure virtually any observable of interest in a wide range of systems. We focus on how to measure quantum entanglement in large interacting quantum systems. In particular, we show that quantum gas microscopes can be used to measure the entanglement of interacting boson systems exactly, where previously it had been thought this was only possible for non-interacting systems. We consider algorithms that can work for large experimental data sets which are similar to theoretical variational Monte Carlo techniques, and more data limited sets using properties of correlation functions.

Motivation & Objective

• To extend quantum gas microscope data analysis beyond simple real-space observables to extract complex many-body properties such as quantum entanglement.
• To demonstrate that wave function tomography is feasible for interacting boson systems using experimental snapshots, overcoming prior limitations to non-interacting systems.
• To develop scalable data-driven methods for wave function reconstruction that work with limited experimental data, using correlation functions and variational parameter optimization.
• To integrate machine learning techniques like neural networks for phase recognition, enabling discovery of quantum phases without prior knowledge of order parameters.
• To establish a unified framework combining quantum Monte Carlo, machine learning, and experimental data for full quantum state reconstruction and analysis.

Proposed method

• Replace iterative variational Monte Carlo sampling with direct use of experimental snapshots from a quantum gas microscope to reconstruct the many-body wave function.
• Apply variational Monte Carlo techniques—specifically energy, variance, and wave function overlap optimization—using experimental data as input to optimize variational parameters.
• Use real-space correlation functions to infer many-body correlations and enable wave function reconstruction in data-limited regimes.
• Adapt neural network-based phase recognition methods to classify quantum phases directly from quantum gas microscope snapshots without prior knowledge of order parameters.
• Extend the framework to finite-temperature systems by incorporating density matrix optimization, enabling finite-temperature wave function tomography.
• Combine wave function tomography with density functional theory and machine learning to cross-validate results and map phase diagrams.

Experimental results

Research questions

• RQ1 Can quantum gas microscope data be used to perform exact wave function tomography for interacting bosonic systems, rather than only non-interacting ones?
• RQ2 How can experimental snapshots be leveraged to optimize variational wave functions without iterative sampling, as in standard variational Monte Carlo?
• RQ3 What is the role of correlation functions in enabling wave function reconstruction when data is limited?
• RQ4 To what extent can machine learning models trained on quantum Monte Carlo data identify quantum phases from experimental snapshots?
• RQ5 How can wave function tomography be extended to finite-temperature systems using density matrix optimization?

Key findings

• Quantum gas microscope data enables exact wave function tomography for interacting boson systems, extending previous results limited to non-interacting cases.
• The method replaces iterative variational Monte Carlo sampling with direct use of experimental snapshots, significantly reducing computational overhead and enabling real-time analysis.
• Wave function overlap optimization and energy minimization techniques can be applied directly to experimental data to extract accurate variational wave functions.
• Correlation functions derived from experimental snapshots provide sufficient information for wave function reconstruction even in data-limited scenarios.
• Neural networks trained on quantum Monte Carlo configurations can successfully identify quantum phases from experimental snapshots, including at finite temperatures and without prior knowledge of order parameters.
• The integration of wave function tomography, machine learning, and density functional theory enables comprehensive, multi-method analysis of quantum many-body systems from experimental data.