On the Correction of Anomalous Phase Oscillation in Entanglement Witnesses Using Quantum Neural Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 25; no. 9; pp. 1696 - 1703
• Main Authors: Behrman, Elizabeth C., Bonde, Richard E. F., Steck, James E., Behrman, Joanna F.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Entanglement; entanglement witness; Indicators; Learning; Mathematical analysis; Neural networks; Oscillations; Oscillators; quantum backpropagation; Quantum computing; Quantum entanglement; quantum neural network (QNN); Quantum theory; supervised learning; Testing; Time measurement; Training; Utilities; Entanglement; entanglement witness; quantum backpropagation; quantum computing; supervised learning; quantum neural network (QNN)
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2013.2281938

Entanglement of a quantum system depends upon the relative phase in complicated ways, which no single measurement can reflect. Because of this, "entanglement witnesses" (measures that estimate entanglement) are necessarily limited in applicability and/or utility. We propose here a solution to the problem using quantum neural networks. A quantum system contains the information of its entanglement; thus, if we are clever, we can extract that information efficiently. As proof of concept, we show how this can be done for the case of pure states of a two-qubit system, using an entanglement indicator corrected for the anomalous phase oscillation. Both the entanglement indicator and the phase correction are calculated by the quantum system itself acting as a neural network.