Classification of four-qubit entangled states via Machine Learning

Abstract

We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication (SLOCC) classification and the description of the four-qubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the entanglement witness problem when the coarse-grained description of a given family state is available. We also discuss and demonstrate the efficiency of nonlinear kernel SVM methods as applied to four-qubit entangled state classification.

10 pages, 8 figures

References in corpus (15)

• Entanglement detection
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Entanglement purification and quantum error correction
• Long-distance entanglement purification for quantum communication
• Towards real-world quantum networks: a review
• Quantum Internet Protocol Stack: a Comprehensive Survey
• Theory of quantum system certification: a tutorial
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Experimental Verification of Multipartite Entanglement in Quantum Networks
• Geometry of faithful entanglement
• On multipartite invariant states I. Unitary symmetry
• Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
• Two-photon amplitude interferometry for precision astrometry
• Dimension-free entanglement detection in multipartite Werner states
• Quantum-Assisted Optical Interferometers: Instrument Requirements

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