Learning Algebraic Models of Quantum Entanglement

TL;DR

This paper explores how deep neural networks can be trained to classify quantum entanglement types by learning algebraic models, enabling efficient detection of entanglement features in multi-qubit and qutrit systems.

Contribution

It introduces neural network-based methods for algebraic classification of quantum entanglement, including border rank and degeneracy detection, advancing quantum state analysis.

Findings

Neural networks can predict entanglement types with high accuracy.

Effective classification for systems up to 5 qubits and 3 qutrits.

Demonstrated ability to detect degenerate and border rank states.

Abstract

We review supervised learning and deep neural network design for learning membership on algebraic varieties. We demonstrate that these trained artificial neural networks can predict the entanglement type for quantum states. We give examples for detecting degenerate states, as well as border rank classification for up to 5 binary qubits and 3 qutrits (ternary qubits).