Zhenghan Wang Explained

Zhenghan Wang
Native Name:王正汉
Birth Date:April 26, 1965.
Birth Place:Tsingtao, China
Fields:Mathematics
Mathematical physics
Workplaces:Microsoft Station Q
UC Santa Barbara
Perimeter Institute
Indiana University Bloomington
University of Michigan
Alma Mater:UC San Diego (PhD)
University of Science and Technology of China (BS, MS)
Thesis Title:The Classification of Topological Four-Manifolds with Infinite Cyclic Fundamental Group
Thesis Url:https://web.math.ucsb.edu/~zhenghwa/data/research/pub/Dissertation-93.pdf
Thesis Year:1993
Doctoral Advisor:Michael Freedman
Known For:Topological quantum computing
Freedman-He-Wang conjecture
Walker-Wang model
Awards:Alexanderson Award (2019)
Website:https://web.math.ucsb.edu/~zhenghwa/

Zhenghan Wang (Chinese: 王正汉; born April 26, 1965) is a Chinese-American mathematician. He is a principal researcher at Microsoft Station Q, as well as a professor of mathematics at the University of California, Santa Barbara.

Education and career

Wang graduated with a B.S. and M.S. from the University of Science and Technology of China in 1989 and obtained his Ph.D. in 1993 from UC San Diego under the supervision of Michael Freedman.[1] From 1993 to 1996 Wang taught as an assistant professor at the University of Michigan and from 1996 to 2007 Wang taught at Indiana University Bloomington. For the majority of this time, Wang specialized in the topology of 4-manifolds.[2] [3]

In 2005, Wang moved to Santa Barbara to serve as a lead scientist in the newly-founded research institute Microsoft Station Q. At Station Q, Wang worked with Michael Freedman (the station's director and his former Ph.D. advisor) on the foundations of topological quantum computing.[4] Since 2012 Wang has served as a full professor at UC Santa Barbara.[1] From 2013 to 2020 Wang served as a distinguished visiting research chair at the Perimeter Institute for Theoretical Physics as well.[1] Wang was included in the 2019 class of fellows of the American Mathematical Society.[5]

Research

Topological Quantum Computing

Zhenghan Wang's most notable contributions are in the field of topological quantum computation. In a series of early papers with Michael Freedman, Michael J. Larsen, and Alexei Kitaev, Wang established the abstract equivalence of topological quantum computation with the quantum circuit model.[6] [7] The implication of these works for topological phases is that the Fibonacci anyon model can be used to make a universal quantum computer, and the implication of these works for quantum circuits is the Aharonov–Jones–Landau algorithm. Wang has also introduced several other schemes for universal topological quantum computation using anyons which are more likely to be experimentally realizable.[8] [9] [10]

The Algebraic Theory of Topological Phases

Outside of direct applications to topological quantum computing, Wang has made many contributions to the formal algebraic theory of two dimensional topological quantum phases of matter. This includes work on the structure and classification of bosonic topological order (modular tensor categories),[11] [12] fermionic topological order (super-modular tensor categories),[13] [14] and symmetry-enriched topological order (G-crossed modular tensor categories).[15] [16] Wang has also worked more specifically on the theory of the fractional quantum Hall effect[17] [18] [19] and anyonic chains.[20] [21] [22]

Higher Dimensional Topological Quantum Field Theory

In addition to his work on two dimensional topological order, Wang has also worked in the theory of three dimensional topological quantum field theory. Here he is most well known introducing the Walker-Wang model along with his coauthor Kevin Walker.[23] [24] This theory has been used to describe the boundaries of topological insulators[25] and to construct nontrivial quantum cellular automata.[26] Wang has also made contributions to the theory of three dimensional fracton phases[27]

Notes and References

  1. Web site: Engineering New Physical Reality: Quantum Computing with Topological Materials . Institute for Optical Science . 12 March 2021 . 30 March 2024.
  2. Wang . Zhenghan . 1995 . CLASSIFICATION OF CLOSED NONORIENTABLE 4-MANIFOLDS WITH INFINITE CYCLIC FUNDAMENTAL GROUP . Mathematical Research Letters . 2 . 3 . 339–344 . 10.4310/MRL.1995.v2.n3.a11 . intlpress.
  3. Wang . Zhenghan . Freedman . Michael . 1994 . CP2-STABLE THEORY . Mathematical Research Letters . 1 . 1 . 4 . intlpress.
  4. Web site: Zhenghan Wang at Microsoft Research . 2024-03-30 . Microsoft Research . en-US.
  5. Web site: Fellows of the American Mathematical Society . 2024-03-30 . American Mathematical Society . en.
  6. Freedman . Michael H. . Kitaev . Alexei . Wang . Zhenghan . 2002-06-01 . Simulation of topological field theories by quantum computers . Communications in Mathematical Physics . 227 . 3 . 587–603 . 10.1007/s002200200635 . quant-ph/0001071 . 2002CMaPh.227..587F . 0010-3616.
  7. Freedman . Michael H. . Larsen . Michael J. . Wang . Zhenghan . 2002-06-01 . The two-eigenvalue problem and density of Jones representation of braid groups . Communications in Mathematical Physics . 228 . 1 . 177–199 . 10.1007/s002200200636 . math/0103200 . 2002CMaPh.228..177F . 0010-3616.
  8. Cui . Shawn X. . Hong . Seung-Moon . Wang . Zhenghan . August 2015 . Universal quantum computation with weakly integral anyons . Quantum Information Processing . 14 . 8 . 2687–2727 . 10.1007/s11128-015-1016-y . 1401.7096 . 2015QuIP...14.2687C . 1570-0755.
  9. Levaillant . Claire . Bauer . Bela . Freedman . Michael . Wang . Zhenghan . Bonderson . Parsa . 2015-07-01 . Universal Gates via Fusion and Measurement Operations on SU$(2)_4$ Anyons . Physical Review A . 92 . 1 . 012301 . 10.1103/PhysRevA.92.012301 . 1504.02098 . 1050-2947.
  10. Cong . Iris . Cheng . Meng . Wang . Zhenghan . 2017-10-25 . Universal Quantum Computation with Gapped Boundaries . Physical Review Letters . 119 . 17 . 170504 . 10.1103/PhysRevLett.119.170504 . 29219455 . 1707.05490 . 2017PhRvL.119q0504C . 0031-9007.
  11. Bruillard . Paul . Ng . Siu-Hung . Rowell . Eric C. . Wang . Zhenghan . 2015-07-21 . Rank-finiteness for modular categories . Journal of the American Mathematical Society . 29 . 3 . 857–881 . 10.1090/jams/842 . 1310.7050 . 0894-0347.
  12. Ng . Siu-Hung . Rowell . Eric C. . Wang . Zhenghan . Wen . Xiao-Gang . September 2023 . Reconstruction of modular data from $SL_2(\mathbb)$ representations . Communications in Mathematical Physics . 402 . 3 . 2465–2545 . 10.1007/s00220-023-04775-w . 2203.14829 . 0010-3616.
  13. Bonderson . Parsa . Rowell . Eric C. . Zhang . Qing . Wang . Zhenghan . 2018-07-16 . Congruence Subgroups and Super-Modular Categories . Pacific Journal of Mathematics . 296 . 2 . 257–270 . 10.2140/pjm.2018.296.257 . 1704.02041 . 0030-8730.
  14. Bruillard . Paul . Galindo . Cesar . Hagge . Tobias . Ng . Siu-Hung . Plavnik . Julia Yael . Rowell . Eric C. . Wang . Zhenghan . 2017-04-01 . Fermionic Modular Categories and the 16-fold Way . Journal of Mathematical Physics . 58 . 4 . 041704 . 10.1063/1.4982048 . 1603.09294 . 2017JMP....58d1704B . 0022-2488.
  15. Barkeshli . Maissam . Bonderson . Parsa . Cheng . Meng . Wang . Zhenghan . 2019-09-20 . Symmetry Fractionalization, Defects, and Gauging of Topological Phases . Physical Review B . 100 . 11 . 115147 . 10.1103/PhysRevB.100.115147 . 1410.4540 . 2019PhRvB.100k5147B . 2469-9950.
  16. Cui . Shawn X. . Galindo . César . Plavnik . Julia Yael . Wang . Zhenghan . December 2016 . On Gauging Symmetry of Modular Categories . Communications in Mathematical Physics . 348 . 3 . 1043–1064 . 10.1007/s00220-016-2633-8 . 1510.03475 . 2016CMaPh.348.1043C . 0010-3616.
  17. Wen . Xiao-Gang . Wang . Zhenghan . 2008-10-09 . Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros . Physical Review B . 78 . 15 . 155109 . 10.1103/PhysRevB.78.155109 . 0803.1016 . 1098-0121.
  18. Peterson . Michael R. . Wu . Yang-Le . Cheng . Meng . Barkeshli . Maissam . Wang . Zhenghan . Sarma . Sankar Das . 2015-07-02 . Abelian and Non-Abelian States in $\nu=2/3$ Bilayer Fractional Quantum Hall Systems . Physical Review B . 92 . 3 . 035103 . 10.1103/PhysRevB.92.035103 . 1502.02671 . 2015PhRvB..92c5103P . 1098-0121.
  19. Lu . Yuan-Ming . Wen . Xiao-Gang . Wang . Zhenghan . Wang . Ziqiang . 2010-03-17 . Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra . Physical Review B . 81 . 11 . 115124 . 10.1103/PhysRevB.81.115124 . 0910.3988 . 2010PhRvB..81k5124L . 1098-0121.
  20. Gils . Charlotte . Ardonne . Eddy . Trebst . Simon . Huse . David A. . Ludwig . Andreas W. W. . Troyer . Matthias . Wang . Zhenghan . 2013-06-17 . Anyonic quantum spin chains: Spin-1 generalizations and topological stability . Physical Review B . 87 . 23 . 235120 . 10.1103/PhysRevB.87.235120 . 1303.4290 . 2013PhRvB..87w5120G . 1098-0121.
  21. Jiang . Hong-Chen . Rachel . Stephan . Weng . Zheng-Yu . Zhang . Shou-Cheng . Wang . Zhenghan . 2010-12-14 . Critical theory of the topological quantum phase transition in a spin-2 chain . Physical Review B . 82 . 22 . 220403 . 10.1103/PhysRevB.82.220403 . 1010.4273 . 1098-0121.
  22. Feiguin . Adrian . Trebst . Simon . Ludwig . Andreas W. W. . Troyer . Matthias . Kitaev . Alexei . Wang . Zhenghan . Freedman . Michael H. . 2007-04-20 . Interacting anyons in topological quantum liquids: The golden chain . Physical Review Letters . 98 . 16 . 160409 . 10.1103/PhysRevLett.98.160409 . 17501404 . cond-mat/0612341 . 2007PhRvL..98p0409F . 0031-9007.
  23. Web site: Walker-Wang model in nLab . 2024-03-23 . ncatlab.org.
  24. Williamson . Dominic J. . Wang . Zhenghan . February 2017 . Hamiltonian models for topological phases of matter in three spatial dimensions . Annals of Physics . 377 . 311–344 . 10.1016/j.aop.2016.12.018 . 1606.07144 . 2017AnPhy.377..311W . 0003-4916.
  25. Burnell . F. J. . Chen . Xie . Fidkowski . Lukasz . Vishwanath . Ashvin . 2014-12-15 . Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order . Physical Review B . 90 . 24 . 245122 . 10.1103/PhysRevB.90.245122 . 1302.7072 . 1098-0121.
  26. Haah . Jeongwan . Fidkowski . Lukasz . Hastings . Matthew B. . February 2023 . Nontrivial Quantum Cellular Automata in Higher Dimensions . Communications in Mathematical Physics . 398 . 1 . 469–540 . 10.1007/s00220-022-04528-1 . 1812.01625 . 2023CMaPh.398..469H . 0010-3616.
  27. Shirley . Wilbur . Slagle . Kevin . Wang . Zhenghan . Chen . Xie . 2018-08-29 . Fracton Models on General Three-Dimensional Manifolds . Physical Review X . 8 . 3 . 031051 . 10.1103/PhysRevX.8.031051 . 1712.05892 . 2018PhRvX...8c1051S . 2160-3308.

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