nLab Alexei Kitaev (changes)

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• Wikipedia entry

Selected writings

On quantum computation and quantum error correction (and stating the Solovay-Kitaev theorem):

• Alexei Kitaev, Quantum computations: algorithms and error correction, Russian Mathematical Surveys, 52 6 (1997) [[doi:10.1070/RM1997v052n06ABEH002155](https://iopscience.iop.org/article/10.1070/RM1997v052n06ABEH002155), pdf]

On quantum circuits with mixed quantum states/density matrices:

• Dorit Aharonov, Alexei Kitaev, Noam Nisan, Quantum Circuits with Mixed States, Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computation (STOC) (1998) 20-30 [[arXiv:quant-ph/9806029](https://arxiv.org/abs/quant-ph/9806029), doi:10.1145/276698.276708]

On quantum error correcting codes associated with planar bulk/boundary systems (precursor to holographic tensor networks):

• S. B. Bravyi, Alexei Kitaev, Quantum codes on a lattice with boundary (arXiv:quant-ph/9811052)

On computation in general and quantum computation in particular:

• Alexei Y. Kitaev, A. H. Shen, M. N. Vyalyi, Classical and Quantum Computation, Graduate Studies in Mathematics 47 (2002) [[doi:10.1090/gsm/047](http://dx.doi.org/10.1090/gsm/047)]

Introducing the idea of topological quantum computation with anyons:

• Alexei Kitaev, Fault-tolerant quantum computation by anyons, Annals Phys. 303 (2003) 2-30 (arXiv:quant-ph/9707021, doi:10.1016/S0003-4916(02)00018-0)

• Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang, Topological quantum computation, Bull. Amer. Math. Soc. 40 (2003), 31-38 (arXiv:quant-ph/0101025, doi:10.1090/S0273-0979-02-00964-3, pdf)

Introducing a model with Majorana zero modes in quantum wires (Kitaev spin chain):

• Alexei Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi, 44 10S (2001) 131-136 [[doi:10.1070/1063-7869/44/10S/S29](https://iopscience.iop.org/article/10.1070/1063-7869/44/10S/S29)]

and its interacting generalization:

• Lukasz Fidkowski, Alexei Kitaev, The effects of interactions on the topological classification of free fermion systems, Phys. Rev. B 81 (2010) 134509 [[arXiv:0904.2197](https://arxiv.org/abs/0904.2197), doi:10.1103/PhysRevB.81.134509]

Comprehensive discussion of anyons:

• Alexei Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321 1 (2006) 2-111 $[$doi:10.1016/j.aop.2005.10.005$]$

On entanglement entropy as an indicator of topological phases of matter:

• Alexei Kitaev, John Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 (arXiv:hep-th/0510092)

On potential experiments detecting uncertainty of fluxes in quantum electromagnetism:

• Alexei Kitaev, Gregory W. Moore, Kevin Walker, Noncommuting Flux Sectors in a Tabletop Experiment [[arXiv:0706.3410](https://arxiv.org/abs/0706.3410)]

On the classification of gapped Hamiltonians/topological insulators by topological K-theory:

• Alexei Kitaev, Periodic table for topological insulators and superconductors, talk at: L.D.Landau Memorial Conference “Advances in Theoretical Physics”, June 22-26, 2008, In:AIP Conference Proceedings 1134, 22 (2009) (arXiv:0901.2686, doi:10.1063/1.3149495)

Introducing the notion of short-range entanglement in quantum materials:

• Alexei Kitaev, Toward Topological Classification of Phases with Short-range Entanglement, talk at KITP (2011) $[$video$]$

• Alexei Kitaev, On the Classification of Short-Range Entangled States , talk at Simons Center (2013) [[video](https://scgp.stonybrook.edu/archives/7874)]$[$video$]$

Discussion of the Levin-Wen model as an extended 3d TQFT formulated using tensor categories:

• Alexei Kitaev, Liang Kong, Levin-Wen models and tensor categories []