Entanglement Classification via Witness Operators generated by Support Vector Machine

Abstract

Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few special cases of higher dimensional systems. In this work, we use a machine learning algorithm, the support vector machine with polynomial kernel, to classify separable and entangled states. We apply it to two-qubit and three-qubit systems, and we show that, after training, the support vector machine is able to recognize if a random state is entangled with an accuracy up to 92% for the two-qubit system and up to 98% for the three-qubit system. We also describe why and in what regime the support vector machine algorithm is able to implement the evaluation of an entanglement witness operator applied to many copies of the state, and we describe how we can translate this procedure into a quantum circuit.

10 pages, 8 figures

References in corpus (7)

• Entanglement detection
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Entangled three-qubit states without concurrence and three-tangle
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Dyson Indices and Hilbert-Schmidt Separability Functions and Probabilities

Cited by in corpus (4)

• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Effect of Weak Measurement Reversal on Quantum Correlations in a Correlated Amplitude Damping Channel, with a Neural Network Perspective
• Entanglement Witness Derived By Using Kolmogorov-Arnold Networks