Current Teaching (Spring 2020)

Math 265, Linear Algebra

Research Interests

low dimensional topology, knot theory, quantum invariants, tensor categories, topological quantum computation, quantum information

Publications and Preprints

Publication list on arXiv and Google scholar

  1. 4-Manifold Invariants From Hopf Algebras. J. Chaidez, J. Cotler, S. X. Cui. 2019. arXiv:1910.14662

  2. Kitaev's quantum double model as an error correcting code. S. X. Cui, D. Ding, X. Han, G. Penington, D. Ranard, B. C. Rayhaun, and Z. Shangnan. 2019. arXiv:1908.02829

  3. The search for leakage-free entangling Fibonacci braiding gates. S. X. Cui, K. T. Tian, J. F. Vasquez, Z. Wang, and H. M. Wong. Journal of Physics A: Mathematical and Theoretical, vol. 52, no. 45, 2019. arXiv:1904.01731

  4. On Generalized Symmetries and Structure of Modular Categories. S. X. Cui, M. Shokrian-Zini, and Z. Wang. SCIENCE CHINA Mathematics, vol. 62, no. 3, pp 417-446, 2019. arXiv:1809.00245

  5. Bit Threads and Holographic Monogamy. S. X. Cui, P. Hayden, T. He, M. Headrick, B. Stoica, and M. Walter. Communications in Mathematical Physics, https://doi.org/10.1007/s00220-019-03510-8, 2019. arXiv:1808.05234

  6. On two quantum invariants of three manifolds from Hopf algebras. L. Chang and S. X. Cui. Advances in Mathematics, vol. 351, pp 621-652, 2019. arXiv:1710.09524

  7. State sum invariants of three manifolds from spherical multi-fusion categories. Z. Wang and S. X. Cui. Journal of Knot Theory and Its Ramifications, vol. 26, no. 14, pp. 1750104, 2017. arXiv:1702.07113

  8. Higher categories and topological quantum field theories. S. X. Cui. Quantum Topology, DOI: 10.4171/QT/128, 2019. arXiv:1610.07628. Note: the published version is titled "Four Dimensional Topological Quantum Field Theories from G-crossed Braided Categories".

  9. Diagonal gates in the Clifford hierarchy. S. X. Cui, D. Gottesman, and A. Krishna. Physical Review A, vol. 95, no. 1, p. 012329, 2017. arXiv:1608.06596

  10. Quantum capacities for entanglement networks. S. X. Cui, Z. Ji, N. Yu, and B. Zeng. IEEE ISIT, 2016. arXiv: 1602.00401

  11. Improved quantum ternary arithmetics. A. Bocharov, S. X. Cui, M. Roetteler, and K. M. Svore. Quantum Information and Computation, vol. 16, no. 9 & 10, 2016. arXiv:1512.03824

  12. On gauging symmetry of modular categories. S. X. Cui, C. Galindo, J. Plavnik, and Z. Wang. Communications in Mathematical Physics, vol. 348, no. 3, pp. 1043-1064, 2016. arXiv:1510.03475

  13. Quantum max-flow/min-cut. S. X. Cui, M. H. Freedman, O. Sattath, R. Stong, and G. Minton. Journal of Mathematical Physics, vol. 57, p. 062206, 2016. arXiv:1508.04644

  14. Efficient topological compilation for weakly-integral anyon model. A. Bocharov, S. X. Cui, V. Kliuchnikov, and Z. Wang. Physical Review A , vol. 93, no. 1, p. 012313, 2016. arXiv:1504.03383

  15. Generalized graph states based on Hadamard matrices. S. X. Cui, N. Yu, and B. Zeng. Journal of Mathematical Physics, vol. 56, no. 3, p. 072201, 2015. arXiv:1502.07195

  16. On enriching the Levin-Wen model with symmetry. L. Chang, M. Cheng, S. X. Cui, Y. Hu, W. Jin, R. Movassagh, P. Naaijkens, Z. Wang, and A. Young. Journal of Physics A: Mathematical and Theoretical, vol. 48, no. 12, p. 12FT01, 2015. arXiv:1412.6589

  17. Framed cord algebra invariant of knots in $S^1 \times S^2$. S. X. Cui and Z. Wang. Journal of Knot Theory and Its Ramifications, vol. 24, no. 14, p. 1550067, 2015. arXiv:1407.8400

  18. Universal quantum computation with metaplectic anyons. S. X. Cui and Z. Wang. Journal of Mathematical Physics, vol. 56, no. 3, p. 032202, 2015. arXiv:1405.7778

  19. Universal quantum computation with weakly integral anyons. S. X. Cui, S. M. Hong, and Z. Wang. Quantum Information Processing, vol. 14, no. 8, pp. 2687-2727, 2015. arXiv:1401.7096

  20. Complexity classes as mathematical axioms II. S. X. Cui, M. H. Freedman, and Z. Wang. Quantum Topology, vol. 7, no. 1, pp. 185-201, 2016. arXiv:1305.6076

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