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Estimating entanglement entropy via variational quantum circuits with classical neural networks
Sangyun Lee1,2, Hyukjoon Kwon3, Jae Sung Lee2
1Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Physical Review. E
|May 17, 2024
Summary
We developed a quantum neural entropy estimator (QNEE) that uses neural networks and quantum circuits to accurately estimate quantum state entropies. QNEE also classifies quantum phases and identifies critical points, aiding quantum information science.
Area of Science:
- Quantum Information Science
- Computational Physics
- Machine Learning
Background:
- Entropy is fundamental in classical and quantum physics, crucial for information science.
- Estimating quantum entropy and classifying quantum phases are challenging but vital tasks.
Purpose of the Study:
- To introduce the Quantum Neural Entropy Estimator (QNEE), a hybrid classical-quantum approach.
- To accurately estimate von Neumann and Rényi entropies of quantum states.
- To classify quantum phases and identify phase transitions using entanglement entropy.
Main Methods:
- Combining classical neural networks (NN) with variational quantum circuits.
- Utilizing QNEE to estimate quantum state entropies, eigenvalues, and eigenstates.
- Applying QNEE to the 1D XXZ Heisenberg model for numerical simulations.
Main Results:
- QNEE accurately estimates quantum entropies and provides eigenvalues/eigenstates.
- The approach successfully classifies quantum phases based on entanglement entropy changes.
- QNEE demonstrates high sensitivity in detecting entanglement entropy near phase transitions.
Conclusions:
- QNEE is an effective tool for quantum entropy estimation and phase classification.
- The hybrid approach offers a powerful method for analyzing complex quantum systems.
- QNEE shows promise for advancing quantum information science and condensed matter physics.
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