Access the full text.
Sign up today, get DeepDyve free for 14 days.
T. Lan, Juven Wang, X. Wen (2014)
Gapped domain walls, gapped boundaries, and topological degeneracy.Physical review letters, 114 7
Liang Kong (2013)
Anyon condensation and tensor categoriesNuclear Physics, 886
A. Davydov, Michael Mueger, D. Nikshych, V. Ostrik (2010)
The Witt group of non-degenerate braided fusion categories, 2013
In the more general case where data qudits are simple objects in a unitary fusion category C , we will label the bulk data qudits as x 1 , x 2 , ... , y 1 , y 2 , ..
M. Gould, T. Lekatsas (2006)
Quasi-Hopf $*$-AlgebrasarXiv: Quantum Algebra
Juven Wang, X. Wen (2012)
Boundary degeneracy of topological orderPhysical Review B, 91
Michael Levin (2013)
Protected edge modes without symmetryarXiv: Strongly Correlated Electrons
A. Kitaev (1997)
Fault tolerant quantum computation by anyonsAnnals of Physics, 303
J. Tits, J. Stillwell (2000)
SymmetryThe American Mathematical Monthly, 107
J. Fröhlich, J. Fuchs, I. Runkel, C. Schweigert (2003)
Correspondences of ribbon categories
A. Kitaev, Liang Kong (2011)
Models for Gapped Boundaries and Domain WallsCommunications in Mathematical Physics, 313
S. Ganeshan, A. Gorshkov, V. Gurarie, V. Galitski (2016)
Exactly soluble model of boundary degeneracy.Physical review. B, 95
In this same general case, the boundary data qudits will be labeled as r 1 , r 2 , ... , s 1 , s 2 ,
M. Barkeshli, J. Sau (2015)
Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana NanowiresarXiv: Mesoscale and Nanoscale Physics
M. Barkeshli, X. Qi (2011)
Topological Nematic States and Non-Abelian Lattice DislocationsarXiv: Strongly Correlated Electrons
All other hom-sets in this category are zero. Furthermore, no idempotent completion is necessary, as all endomorphism spaces in Q
Iris Cong, M. Cheng, Zhenghan Wang (2017)
Universal Quantum Computation with Gapped Boundaries.Physical review letters, 119 17
T. Neupert, T. Neupert, Huan He, C. Keyserlingk, G. Sierra, B. Bernevig (2016)
No-go theorem for boson condensation in topologically ordered quantum liquidsNew Journal of Physics, 18
J. Fuchs, I. Runkel, C. Schweigert (2004)
TFT construction of RCFT correlators IV: Structure constants and correlation functionsNuclear Physics, 715
M. Müger (2004)
Galois extensions of braided tensor categories and braided crossed G-categoriesJ. Algebra, 277
(2009)
Bose-condensation and edges of topological quantum phases. Talk at modular categories and applications
A. Kapustin, N. Saulina (2010)
Topological boundary conditions in abelian Chern-Simons theoryNuclear Physics, 845
Shawn Cui, Seung-Moon Hong, Zhenghan Wang (2014)
Universal quantum computation with weakly integral anyonsQuantum Information Processing, 14
HAMILTONIAN AND ALGEBRAIC THEORIES OF GAPPED BOUNDARIES
Yidun Wan, Chenjie Wang (2016)
Fermion condensation and gapped domain walls in topological ordersJournal of High Energy Physics, 2017
Vahid Karimipour, J. Preskill (1998)
Topological Quantum Computation
Shlomo Gelaki, D. Naidu (2007)
Some properties of group-theoretical categoriesarXiv: Quantum Algebra
V. Ostrik (2002)
Module categories over the Drinfeld double of a finite groupInternational Mathematics Research Notices, 2003
P. Cochat, L. Vaucoret, J. Sarles (2008)
Et alEvidence Based Mental Health, 11
J. Fuchs, C. Schweigert, A. Valentino (2013)
A Geometric Approach to Boundaries and Surface Defects in Dijkgraaf–Witten TheoriesCommunications in Mathematical Physics, 332
Ozhigov Yuriy, Khrennikov Andrei (2020)
Quantum computer
M. Barkeshli, Parsa Bonderson, M. Cheng, Zhenghan Wang (2014)
Symmetry fractionalization, defects, and gauging of topological phasesPhysical Review B
Excitations on the boundary will be labeled as α, β, γ, ... . When necessary, the local degrees of freedom during condensation will be labeled as µ, ν, λ, ...
M. Barkeshli, Chao-Ming Jian, X. Qi (2012)
Twist defects and projective non-Abelian braiding statisticsPhysical Review B, 87
Liang-Chu Chang, M. Cheng, Shawn Cui, Yuting Hu, W. Jin, R. Movassagh, Pieter Naaijkens, Zhenghan Wang, Amanda Young (2014)
On enriching the Levin–Wen model with symmetryJournal of Physics A: Mathematical and Theoretical, 48
J. Fuchs, C. Schweigert, A. Valentino (2012)
Bicategories for Boundary Conditions and for Surface Defects in 3-d TFTCommunications in Mathematical Physics, 321
A. Kirillov, V. Ostrik (2002)
On a q-Analogue of the McKay Correspondence and the ADE Classification of sl̂2 Conformal Field TheoriesAdvances in Mathematics, 171
J. Fuchs, I. Runkel, C. Schweigert (2002)
TFT construction of RCFT correlators I: Partition functionsarXiv: High Energy Physics - Theory
F. Bais, J. Slingerland (2008)
Condensate-induced transitions between topologically ordered phasesPhysical Review B, 79
V. Petkova, J. Zuber (2001)
The many faces of Ocneanu cellsNuclear Physics, 603
B. Bakalov, A. Kirillov (2000)
Lectures on tensor categories and modular functors, 21
Yongchang Zhu (2001)
Hecke algebras and Representation Rings of Hopf algebras
I. Eliens, J. Romers, F. Bais (2013)
Diagrammatics for Bose condensation in anyon theoriesPhysical Review B, 90
V. Ostrik (2001)
Module categories, weak Hopf algebras and modular invariantsTransformation Groups, 8
A. Davydov (2013)
Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifoldsJournal of Mathematical Physics, 55
A. Fowler, M. Mariantoni, J. Martinis, A. Cleland (2012)
Surface codes: Towards practical large-scale quantum computationPhysical Review A, 86
Liang-Chu Chang (2013)
Kitaev models based on unitary quantum groupoidsJournal of Mathematical Physics, 55
P. Etingof, D. Nikshych, V. Ostrik (2002)
On fusion categoriesAnnals of Mathematics, 162
P. Schauenburg (2002)
Hopf Algebra Extensions and Monoidal Categories
Michael Mueger (2002)
Galois extensions of braided tensor categories and braided crossed G-categoriesJournal of High Energy Physics
H. Bombin, M. Martin-Delgado (2008)
Nested topological orderNew Journal of Physics, 13
Michael Levin, X. Wen (2004)
String-net condensation: A physical mechanism for topological phasesPhysical Review B, 71
S. Bravyi, A. Kitaev (1998)
Quantum codes on a lattice with boundaryarXiv: Quantum Physics
Liang Kong (2012)
Some universal properties of Levin-Wen modelsarXiv: Strongly Correlated Electrons
J. Varona (2006)
Rational values of the arccosine functionCentral European Journal of Mathematics, 4
M. Barkeshli, Chao-Ming Jian, X. Qi (2013)
Theory of defects in Abelian topological statesPhysical Review B, 88
A. Kapustin, N. Saulina (2010)
Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field TheoryarXiv: High Energy Physics - Theory
E. Riehl, Dominic Verity (2018)
∞-Categories for the Working Mathematician
Liang Kong, X. Wen, Hao Zheng (2015)
Boundary-bulk relation for topological orders as the functor mapping higher categories to their centersarXiv: Strongly Correlated Electrons
Ling-Yan Hung, Yidun Wan (2014)
Ground-state degeneracy of topological phases on open surfaces.Physical review letters, 114 7
The data qudits in the bulk will be labeled as g 1 , g 2 , ... , h 1 , h 2 , ... for the Kitaev model, where they are members of a finite group G
N. Lindner, E. Berg, G. Refael, A. Stern (2012)
Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall statesarXiv: Mesoscale and Nanoscale Physics
D. Clarke, J. Alicea, K. Shtengel (2012)
Exotic non-Abelian anyons from conventional fractional quantum Hall statesNature Communications, 4
Bulk excitations (a.k.a. anyons or topological charges), which are the simple objects within the modular tensor category B = Z (Rep( G )) or B = Z ( C )
E. Dennis, A. Kitaev, A. Landahl, J. Preskill (2001)
Topological quantum memoryJournal of Mathematical Physics, 43
Michael Mueger (2012)
Modular Categories
M. Barkeshli, Chao-Ming Jian, X. Qi (2013)
Classification of Topological Defects in Abelian Topological StatesPhysical Review B, 88
M. Cheng (2012)
Superconducting Proximity Effect on the Edge of Fractional Topological InsulatorsPhysical Review B, 86
P. Schauenburg (2002)
Hopf modules and the double of a quasi-Hopf algebraTransactions of the American Mathematical Society, 354
X. Wen (1989)
Vacuum degeneracy of chiral spin states in compactified space.Physical review. B, Condensed matter, 40 10
T. Neupert, Huan He, C. Keyserlingk, G. Sierra, A. Bernevig (2016)
Boson condensation in topologically ordered quantum liquidsPhysical Review B, 93
H. Bombin, M. Martin-Delgado (2007)
Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinementPhysical Review B, 78
Cristopher Moore, D. Rockmore, A. Russell (2003)
Generic quantum Fourier transforms
Iris Cong, M. Cheng, Zhenghan Wang (2016)
Topological Quantum Computation with Gapped BoundariesarXiv: Quantum Physics
P. Schauenburg (2015)
Computing Higher Frobenius-Schur Indicators in Fusion Categories Constructed from Inclusions of Finite GroupsarXiv: Quantum Algebra
C. Nayak, S. Simon, A. Stern, M. Freedman, S. Sarma (2007)
Non-Abelian Anyons and Topological Quantum ComputationReviews of Modern Physics, 80
M. Freedman (1998)
P/NP, and the quantum field computerProceedings of the National Academy of Sciences of the United States of America, 95 1
Iris Cong, M. Cheng, Zhenghan Wang (2017)
Defects between gapped boundaries in two-dimensional topological phases of matterPhysical Review B, 96
A. Kapustin (2013)
Ground-state degeneracy for Abelian anyons in the presence of gapped boundariesPhysical Review B, 89
D. Naidu, E. Rowell (2009)
A Finiteness Property for Braided Fusion CategoriesAlgebras and Representation Theory, 14
J. Varona (2006)
Rational values of the arccosine functionOpen Math., 4
We can determine gapped boundary types of the D(S 3 ) model by computing all Lagrangian algebras in B, using the procedure of Section 3.2. This gives four gapped boundary types
R. Raussendorf, D. Browne, H. Briegel (2003)
Measurement-based quantum computation on cluster statesPhysical Review A, 68
Salman Beigi, P. Shor, Daniel Whalen (2010)
The Quantum Double Model with Boundary: Condensations and SymmetriesCommunications in Mathematical Physics, 306
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev’s quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.
Communications in Mathematical Physics – Springer Journals
Published: Jul 11, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.