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Celebratio Mathematica

Michael H. Freedman

Topology; quantum computing  ·  UCSD & Microsoft

Quantum computing

[1] article M. H. Freed­man: “P/NP, and the quantum field com­puter,” Proc. Natl. Acad. Sci. USA 95 : 1 (1998), pp. 98–​101. MR 1612425 Zbl 0895.​68053

[2] incollection M. H. Freed­man: “To­po­lo­gic­al views on com­pu­ta­tion­al com­plex­ity,” pp. 453–​464 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Ber­lin, 1998), published as Doc. Math. Ex­tra II. Fak­ultät für Math­em­atik, Uni­versität Biele­feld (Biele­feld), 1998. MR 1648095 Zbl 0967.​68520

[3] incollection M. H. Freed­man: “\( K \)-sat on groups and un­de­cid­ab­il­ity,” pp. 572–​576 in Pro­ceed­ings of the thir­ti­eth an­nu­al ACM sym­posi­um on the­ory of com­put­ing (Dal­las, TX, May 23–26, 1998). Edi­ted by Association for Computing Machinery. As­so­ci­ation for Com­put­ing Ma­chinery (New York), 1998. MR 1715605 Zbl 1028.​68068

[4] article M. H. Freed­man and D. A. Mey­er: “Pro­ject­ive plane and planar quantum codes,” Found. Com­put. Math. 1 : 3 (2001), pp. 325–​332. MR 1838758 Zbl 0995.​94037 ArXiv quant-​ph/​9810055

[5] article M. H. Freed­man: “Quantum com­pu­ta­tion and the loc­al­iz­a­tion of mod­u­lar func­tors,” Found. Com­put. Math. 1 : 2 (2001), pp. 183–​204. MR 1830035 Zbl 1004.​57026 ArXiv quant-​ph/​0003128

[6] article M. H. Freed­man, M. J. Larsen, and Z. Wang: “The two-ei­gen­value prob­lem and dens­ity of Jones rep­res­ent­a­tion of braid groups,” Comm. Math. Phys. 228 : 1 (2002), pp. 177–​199. MR 1911253 Zbl 1045.​20027

[7] article M. H. Freed­man, M. Larsen, and Z. Wang: “A mod­u­lar func­tor which is uni­ver­sal for quantum com­pu­ta­tion,” Comm. Math. Phys. 227 : 3 (2002), pp. 605–​622. MR 1910833 Zbl 1012.​81007 ArXiv quant-​ph/​0001108

[8] article M. H. Freed­man, A. Kit­aev, and Z. Wang: “Sim­u­la­tion of to­po­lo­gic­al field the­or­ies by quantum com­puters,” Comm. Math. Phys. 227 : 3 (2002), pp. 587–​603. MR 1910832 Zbl 1014.​81006 ArXiv quant-​ph/​0001071

[9] article M. H. Freed­man: “Poly-loc­al­ity in quantum com­put­ing,” Found. Com­put. Math. 2 : 2 (2002), pp. 145–​154. MR 1894373 Zbl 1075.​81507 ArXiv quant-​ph/​0001077

[10] incollection M. H. Freed­man, D. A. Mey­er, and F. Luo: “\( Z_2 \)-systol­ic free­dom and quantum codes,” pp. 287–​320 in Math­em­at­ics of quantum com­pu­ta­tion. Edi­ted by R. K. Bryl­in­ski and G. Chen. Com­pu­ta­tion­al Math­em­at­ics 3. Chap­man & Hall/CRC (Boca Raton, FL), 2002. MR 2007952 Zbl 1075.​81508

[11] article M. H. Freed­man: “A mag­net­ic mod­el with a pos­sible Chern–Si­mons phase,” Comm. Math. Phys. 234 : 1 (2003), pp. 129–​183. With an ap­pendix by F. Good­man and H. Wen­zl. MR 1961959 Zbl 1060.​81054 ArXiv quant-​ph/​0110060

[12] article M. H. Freed­man, A. Kit­aev, M. J. Larsen, and Z. Wang: “To­po­lo­gic­al quantum com­pu­ta­tion,” Bull. Amer. Math. Soc. (N.S.) 40 : 1 (2003), pp. 31–​38. MR 1943131 Zbl 1019.​81008 ArXiv quant-​ph/​0101025

[13] techreport M. H. Freed­man, C. Nayak, and K. Shten­gel: Non-Abeli­an to­po­lo­gic­al phases in an ex­ten­ded Hub­bard mod­el. Pre­print, September 2003. ArXiv cond-​mat/​0309120

[14] article M. Freed­man, C. Nayak, K. Shten­gel, K. Walk­er, and Z. Wang: “A class of \( P,T \)-in­vari­ant to­po­lo­gic­al phases of in­ter­act­ing elec­trons,” Ann. Phys­ics 310 : 2 (2004), pp. 428–​492. MR 2044743 Zbl 1057.​81053

[15] article M. Bor­dewich, M. Freed­man, L. Lovász, and D. Welsh: “Ap­prox­im­ate count­ing and quantum com­pu­ta­tion,” Com­bin. Probab. Com­put. 14 : 5–​6 (2005), pp. 737–​754. MR 2174653 Zbl 1089.​68040

[16]M. H. Freed­man, C. Nayak, and K. Shten­gel: “Line of crit­ic­al points in \( 2+1 \) di­men­sions: Quantum crit­ic­al loop gases and non-abeli­an gauge the­ory,” Phys. Rev. Lett. 94 : 14 (2005), pp. 147205.

[17] article D. Das Sarma, M. H. Freed­man, and C. Nayak: “To­po­lo­gic­ally-pro­tec­ted qubits from a pos­sible non-abeli­an frac­tion­al quantum Hall state,” Phys. Rev. Lett. 94 : 6 (2005), pp. 166802. ArXiv cond-​mat/​0412343

[18]M. Freed­man, C. Nayak, and K. Shten­gel: “An ex­ten­ded Hub­bard mod­el with ring ex­change: A route to a non-abeli­an to­po­lo­gic­al phase,” Phys. Rev. Lett. 94 : 6 (2005), pp. 066401.

[19] techreport M. Freed­man, C. Nayak, and K. Walk­er: Tilted in­ter­fer­o­metry real­izes uni­ver­sal quantum com­pu­ta­tion in the Ising TQFT without over­passes. Pre­print, December 2005. ArXiv cond-​mat/​0512072

[20]M. Freed­man, C. Nayak, and K. Walk­er: “To­wards uni­ver­sal to­po­lo­gic­al quantum com­pu­ta­tion in the \( \nu=5/2 \) frac­tion­al quantum Hall state,” Phys. Rev. B 73 : 24 (2006), pp. 245307.

[21]M. Freed­man, S. Das Sarma, and C. Nayak: “To­po­lo­gic­al quantum com­pu­ta­tion,” Phys­ics Today 59 : 7 (July 2006), pp. 32–​38.

[22] article S. H. Si­mon, N. E. Bonesteel, M. H. Freed­man, N. Pet­ro­vic, and L. Hor­mozi: “To­po­lo­gic­al quantum com­put­ing with only one mo­bile qua­si­particle,” Phys. Rev. Lett. 96 : 7 (2006), pp. 070503. MR 2205654 ArXiv quant-​ph/​0509175

[23] article M. Freed­man, A. Feiguin, S. Trebst, A. Lud­wig, M. Troy­er, A. Kit­aev, and Z. Wang: “In­ter­act­ing any­ons in to­po­lo­gic­al quantum li­quids: The golden chain,” Phys. Rev. Lett. 98 (2007), pp. 160409. ArXiv cond-​mat/​0612341

[24] article M. H. Freed­man and Z. Wang: “Large quantum Four­i­er trans­forms are nev­er ex­actly real­ized by braid­ing con­form­al blocks,” Phys. Rev. A (3) 75 : 3 (2007), pp. 032322. MR 2312110 ArXiv cond-​mat/​0609411

[25] article P. Bon­der­son, M. Freed­man, and C. Nayak: “Meas­ure­ment-only to­po­lo­gic­al quantum com­pu­ta­tion,” Phys. Rev. Lett. 101 : 1 (2008), pp. 010501. MR 2429542 Zbl 1228.​81121 ArXiv 0802.​0279

[26] article C. Nayak, S. H. Si­mon, A. Stern, M. Freed­man, and S. Das Sarma: “Non-abeli­an any­ons and to­po­lo­gic­al quantum com­pu­ta­tion,” Rev. Mod­ern Phys. 80 : 3 (2008), pp. 1083–​1159. MR 2443722 Zbl 1205.​81062 ArXiv 0707.​1889

[27]M. Freed­man, C. Nayak, and K. Shten­gel: “Lieb–Schultz–Mat­tis the­or­em for qua­s­ito­po­lo­gic­al sys­tems,” Phys. Rev. B 78 (2008), pp. 174411.

[28] incollection M. Freed­man, C. Nayak, K. Walk­er, and Z. Wang: “On pic­ture \( (2+1) \)-TQFTs,” pp. 19–​106 in To­po­logy and phys­ics (Tianjin, China, 27–31 Ju­ly 2007). Edi­ted by K. Lin, Z. Weng, and W. Zhang. Nankai Tracts in Math­em­at­ics 12. World Sci­entif­ic (Hack­en­sack, NJ), 2008. MR 2503392 Zbl 1168.​81024 ArXiv 0806.​1926

[29] techreport M. H. Freed­man: A to­po­lo­gic­al phase in a quantum grav­ity mod­el. Pre­print, December 2008. A talk at Solvay con­fer­ence, Oc­to­ber 2008. ArXiv 0812.​2278

[30] article P. Bon­der­son, M. Freed­man, and C. Nayak: “Meas­ure­ment-only to­po­lo­gic­al quantum com­pu­ta­tion via any­on­ic in­ter­fer­o­metry,” Ann. Phys­ics 324 : 4 (2009), pp. 787–​826. MR 2508474 Zbl 1171.​81004 ArXiv 0808.​1933

[31] article L. Fidkowski, M. Freed­man, C. Nayak, K. Walk­er, and Z. Wang: “From string nets to nona­beli­ons,” Comm. Math. Phys. 287 : 3 (2009), pp. 805–​827. MR 2486662 Zbl 1196.​82072 ArXiv cond-​mat/​0610583

[32] techreport P. Bon­der­son, S. Das Sarma, M. Freed­man, and C. Nayak: A blue­print for a to­po­lo­gic­ally fault-tol­er­ant quantum com­puter. Pre­print, March 2010. ArXiv 1003.​2856

[33] article M. H. Freed­man, L. Gamper, C. Gils, S. V. Isakov, S. Trebst, and M. Troy­er: “To­po­lo­gic­al phases: An ex­ped­i­tion off lat­tice,” Ann. Phys­ics 326 : 8 (2011), pp. 2108–​2137. MR 2812881 Zbl 1221.​81219 ArXiv 1102.​0270

[34] techreport S. J. Yamamoto, M. Freed­man, and K. Yang: 3D non-abeli­an any­ons: De­gen­er­acy split­ting and de­tec­tion by adia­bat­ic cool­ing. Pre­print, February 2011. ArXiv 1102.​5742

[35] article M. Freed­man, M. B. Hast­ings, C. Nayak, X.-L. Qi, K. Walk­er, and Z. Wang: “Pro­ject­ive rib­bon per­muta­tion stat­ist­ics: A rem­nant of non-Abeli­an braid­ing in high­er di­men­sions,” Phys. Rev. B 83 : 11 (2011), pp. 115132. ArXiv 1005.​0583