Machine-Learning-Derived Entanglement Witnesses

TL;DR

This paper introduces a machine learning approach using support vector machines to generate efficient entanglement witnesses that require fewer measurements, demonstrated on quantum hardware.

Contribution

It establishes a novel correspondence between SVMs and entanglement witnesses, enabling systematic construction and optimization of witnesses for complex quantum states.

Findings

SVM-derived witnesses can detect entanglement with fewer measurements.

The method works for bipartite and tripartite qubits and qudits.

Demonstrated successful implementation on IBM Quantum hardware.

Abstract

In this work, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states. An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target entangled state; this hyperplane is a weighted sum of observables ('features') whose coefficients are optimized during the training of the SVM. We demonstrate with this method the ability to obtain witnesses that require only local measurements even when the target state is a non-stabilizer state. Furthermore, we show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This allows us to derive W state witnesses capable of detecting entanglement with fewer measurement terms than the fidelity method dominant in today's literature. The utility of this approach is demonstrated on quantum hardware furnished through the IBM Quantum Experience.