https://doi.org/10.1140/epjp/s13360-023-04546-5
Regular Article
Entanglement classification via witness operators generated by support vector machine
1
Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40127, Bologna, Italy
2
Sezione di Bologna, INFN, 40127, Bologna, Italy
3
Leithà S.r.l. | Unipol Group, 610101, Bologna, Italy
Received:
27
July
2023
Accepted:
2
October
2023
Published online:
21
October
2023
Although entanglement is a basic resource for reaching quantum advantage 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 
for the two-qubit system and up to 
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.
© The Author(s) 2023
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