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Experimental measurement of bipartite entanglement using parameterized quantum circuits

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Abstract

Entanglement in quantum systems plays a crucial role in various quantum information tasks. Measuring entanglement has been an important issue in both experiments and theories. In this work, we use parameterized quantum circuits (PQCs) to diagonalize density matrices of quantum states and obtain entanglement by only measuring the diagonal elements. With this method, full quantum state tomography can be bypassed, greatly reducing the number of measurements. A comprehensive characterization of entanglement was performed by using Rényi entropy and partially transposed moments. Mutual information, calculated from entropy is also used to characterize dynamical quantum phase transitions. We experimentally demonstrated the method on a four-qubit nuclear magnetic resonance quantum simulator. Our results agree with the theoretical descriptions. The measurement complexity of our PQC-based method grows linearly with the number of diagonal elements in the density matrix, a square root reduction over the full quantum tomography. The proposed method can have great potential in quantum systems with a large number of particles.

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Correspondence to Dawei Lu or Tao Xin.

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This work was supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0303700, and 2019YFA0308100), National Natural Science Foundation of China (Grant Nos. 12075110, 11975117, 11905099, 11875159, U1801661, and 11774197), Key R&D Program of Guangdong Province (Grant No. 2018B030325002), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019A1515011383), Guangdong International Collaboration Program (Grant No. 2020A0505100001), Guangdong Provincial Key Laboratory (Grant No. 2019B121203002), Science, Technology and Innovation Commission of Shenzhen Municipality (Grant Nos. ZDSYS20170303165926217, KQTD20190929173815000, JCYJ20200109140803865, JCYJ20170412152620376, and JCYJ20180302174036418), and Tsinghua University Initiative Scientific Research Program, Beijing Advanced Innovation Center for Future Chip (ICFC), Pengcheng Scholars, Guangdong Innovative and Entrepreneurial Research Team Program (Grant No. 2019ZT08C044).

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Xue, S., Huang, Y., Zhao, D. et al. Experimental measurement of bipartite entanglement using parameterized quantum circuits. Sci. China Phys. Mech. Astron. 65, 280312 (2022). https://doi.org/10.1007/s11433-022-1904-3

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