Reinforcement-learning generation of four-qubit entangled states

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We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with four qubits. This way, the algorithm is able to generate representative states for some of the 49 true SLOCC classes of the four-qubit entanglement states. In particular, it is possible to reach at least one true SLOCC class for each of the nine entanglement families. The quantum circuits synthesized by the algorithm may be useful for the experimental realization of these important classes of entangled states and to draw conclusions about the intrinsic properties of our universe. We introduce a graphical tool called the state-link graph (SLG) to represent the construction of the quality matrix (Q-matrix) used by the algorithm to build a given objective state belonging to the corresponding entanglement class. This allows us to discover the necessary connections between specific entanglement features and the role of certain quantum gates, which the algorithm needs to include in the quantum gate set of actions. The quantum circuits found are optimal by construction with respect to the quantum gate-set chosen. These SLGs make the algorithm simple, intuitive, and a useful resource for the automated construction of entangled states with a low number of qubits.
© The Autor(s) 2022 We acknowledge support from the CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM), Spanish MINECO grants MINECO/FEDER Projects, PGC2018-099169-B-I00 FIS2018, MCIN with funding from European Union Next Generation EU (PRTR-C17.I1) an Ministry of Economic Affairs Quantum ENIA project. M. A. M.-D. has been partially supported by the U.S. Army Research Office through Grant No. W911NF-14-1-0103. S.G. acknowledges support from a QUITEMAD grant. We acknowledge the precious support of R. Fazio (ICTP and Universita degli studi di Napoli "Federico II"), P. Lucignano (Universita degli studi di Napoli"Federico II") and the Universita degli studi di Napoli "Fed-erico II."
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