nLab Alexei Kitaev

Alexei Yurievich Kitaev

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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, 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, 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]

On quantum measurement of Wilson loops:

• David Beckman, Daniel Gottesman, Alexei Kitaev, John Preskill: Measurability of Wilson loop operators, Phys. Rev. D 65 (2002) 065022 [arXiv:hep-th/0110205, doi:10.1103/PhysRevD.65.065022]

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, arXiv:cond-mat/0010440]

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, 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]

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 and conjecturing its classification by spaces forming an Omega-spectrum:

• 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]

• Alexei Kitaev: Homotopy-theoretic approach to SPT phases in action: $\mathbb{Z}_{16}$ classification of three-dimensional superconductors, Talk at: Symmetry and Topology in Quantum Matter Workshop, Institute for Pure and Applied Mathematics, University of California (2015) [web]

• Alexei Kitaev: Topological quantum phases, Talk at IAS (2019) [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 [pdf]

category: people