Quantum Information Meets Quantum Matter

[1]  Norbert Schuch,et al.  Characterizing Topological Order with Matrix Product Operators , 2014, Annales Henri Poincaré.

[2]  A. Lichnerowicz Proof of the Strong Subadditivity of Quantum-Mechanical Entropy , 2018 .

[3]  J. S. BELLt Einstein-Podolsky-Rosen Paradox , 2018 .

[4]  John McGreevy,et al.  Renormalization group constructions of topological quantum liquids and beyond , 2014, 1407.8203.

[5]  E. Tonni,et al.  Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations , 2015, 1501.04311.

[6]  Wei Zhu,et al.  Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice , 2014, 1412.1571.

[7]  W. Zhu,et al.  Chiral and Critical Spin Liquids in Spin-1/2 Kagome Antiferromagnet , 2014, 1410.4883.

[8]  B. Zeng,et al.  Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity , 2014, 1406.5090.

[9]  T. Han,et al.  High-field magnetic ground state in S = 1 2 kagome lattice antiferromagnet ZnCu 3 ( OH ) 6 Cl 2 , 2014 .

[10]  B. Zeng,et al.  Topological and error-correcting properties for symmetry-protected topological order , 2014, 1407.3413.

[11]  Zitao Wang,et al.  Fermionic symmetry protected topological phases and cobordisms , 2014, Journal of High Energy Physics.

[12]  Chi-Kwong Li,et al.  Discontinuity of maximum entropy inference and quantum phase transitions , 2014, 1406.5046.

[13]  X. Wen,et al.  Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions , 2014, 1405.5858.

[14]  B. Zeng,et al.  Irreducible many-body correlations in topologically ordered systems , 2014, 1402.4245.

[15]  D. Sheng,et al.  Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model. , 2013, Physical review letters.

[16]  X. Wen,et al.  Topological quasiparticles and the holographic bulk-edge relation in (2+1) -dimensional string-net models , 2013, 1311.1784.

[17]  Jeongwan Haah Bifurcation in entanglement renormalization group flow of a gapped spin model , 2013, 1310.4507.

[18]  Bei Zeng,et al.  Symmetric extension of two-qubit states , 2013, 1310.3530.

[19]  O. Buerschaper Twisted injectivity in projected entangled pair states and the classification of quantum phases , 2013, 1307.7763.

[20]  Roman Orus,et al.  Geometric entanglement in topologically ordered states , 2013, 1304.1339.

[21]  Xiao-Gang Wen,et al.  Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory , 2012, 1201.2648.

[22]  H. Bombin,et al.  An Introduction to Topological Quantum Codes , 2013, 1311.0277.

[23]  Aram W. Harrow,et al.  The Church of the Symmetric Subspace , 2013, 1308.6595.

[24]  Umesh Vazirani,et al.  A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians , 2013, 1307.5143.

[25]  Daniel Nagaj,et al.  Quantum 3-SAT Is QMA1-Complete , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[26]  Umesh Vazirani,et al.  An area law and sub-exponential algorithm for 1D systems , 2013, 1301.1162.

[27]  X. Qi,et al.  Momentum polarization: An entanglement measure of topological spin and chiral central charge , 2012, 1212.6951.

[28]  M. Zaletel,et al.  Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians. , 2012, Physical review letters.

[29]  Yidun Wan,et al.  Twisted quantum double model of topological phases in two dimensions , 2012, 1211.3695.

[30]  Yi Zhang,et al.  Establishing non-Abelian topological order in Gutzwiller-projected Chern insulators via entanglement entropy and modular S-matrix , 2012, 1209.2424.

[31]  L. Cincio,et al.  Characterizing topological order by studying the ground States on an infinite cylinder. , 2012, Physical review letters.

[32]  Xiao-Gang Wen,et al.  Symmetry protected topological orders and the group cohomology of their symmetry group , 2011, 1106.4772.

[33]  Xiao-Gang Wen,et al.  Symmetry-Protected Topological Orders in Interacting Bosonic Systems , 2012, Science.

[34]  Yidun Wan,et al.  String-net models withZNfusion algebra , 2012, 1207.6169.

[35]  Christopher Mudry,et al.  Enhancing the stability of a fractional Chern insulator against competing phases , 2012 .

[36]  Leon Balents,et al.  Identifying topological order by entanglement entropy , 2012, Nature Physics.

[37]  Frank Pollmann,et al.  Detection of symmetry-protected topological phases in one dimension , 2012, 1204.0704.

[38]  Tzu-Chieh Wei,et al.  Quantum Computation by Local Measurement , 2012, 1208.0041.

[39]  David Pérez-García,et al.  Order parameter for symmetry-protected phases in one dimension. , 2012, Physical review letters.

[40]  R. Moessner,et al.  Spin Ice, Fractionalization, and Topological Order , 2011, 1112.3793.

[41]  U. Vazirani,et al.  Improved one-dimensional area law for frustration-free systems , 2011, 1111.2970.

[42]  Yi Zhang,et al.  Quasiparticle statistics and braiding from ground state entanglement , 2011, 1111.2342.

[43]  Yuting Hu,et al.  Ground State Degeneracy in the Levin-Wen Model for Topological Phases , 2011, 1105.5771.

[44]  Liang Kong,et al.  Models for Gapped Boundaries and Domain Walls , 2011, 1104.5047.

[45]  Frank Pollmann,et al.  Symmetry protection of topological phases in one-dimensional quantum spin systems , 2009, 0909.4059.

[46]  Zhaohui Wei,et al.  Measurement-Based Quantum Computing with Valence-Bond-Solids , 2011, 1111.5084.

[47]  David Pérez-García,et al.  Classifying quantum phases using matrix product states and projected entangled pair states , 2011 .

[48]  A. Seidel,et al.  Abelian and Non-Abelian Statistics in the Coherent State Representation , 2011, 1108.2734.

[49]  Xiao-Gang Wen,et al.  Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations , 2011, 1106.4752.

[50]  K. Walker,et al.  (3+1)-TQFTs and topological insulators , 2011, 1104.2632.

[51]  Ying Ran,et al.  Z 2 spin liquids in the S=(1)/(2) Heisenberg model on the kagome lattice: A projective symmetry-group study of Schwinger fermion mean-field states , 2011, 1104.1432.

[52]  Xiao-Gang Wen,et al.  Complete classification of one-dimensional gapped quantum phases in interacting spin systems , 2011, 1103.3323.

[53]  Y. Lee,et al.  Local spin susceptibility of the S=(1)/(2) kagome lattice in ZnCu 3 (OD) 6 Cl 2 , 2011, 1103.2457.

[54]  L. Sheng,et al.  Fractional quantum Hall effect in the absence of Landau levels , 2011, Nature communications.

[55]  Matthew B. Hastings,et al.  Topological entanglement entropy of a Bose-Hubbard spin liquid , 2011, 1102.1721.

[56]  Jeongwan Haah Local stabilizer codes in three dimensions without string logical operators , 2011, 1101.1962.

[57]  C. Chamon,et al.  Fractional quantum Hall states at zero magnetic field. , 2010, Physical review letters.

[58]  Xiao-Gang Wen,et al.  High-temperature fractional quantum Hall states. , 2010, Physical review letters.

[59]  Zhengfeng Ji,et al.  complete characterization of the ground-space structure of two-body frustration-free hamiltonians for qubits , 2010, 1010.2480.

[60]  Frank Pollmann,et al.  Topological Phases of One-Dimensional Fermions: An Entanglement Point of View , 2010, 1008.4346.

[61]  Alexei Kitaev,et al.  Topological phases of fermions in one dimension , 2010, 1008.4138.

[62]  Xiao-Gang Wen,et al.  Classification of gapped symmetric phases in one-dimensional spin systems , 2010, 1008.3745.

[63]  S. Bravyi Subsystem codes with spatially local generators , 2010, 1008.1029.

[64]  Beni Yoshida,et al.  Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes , 2010, 1007.4601.

[65]  Maissam Barkeshli,et al.  Correlated topological insulators and the fractional magnetoelectric effect , 2010, 1005.1076.

[66]  Runyao Duan,et al.  No-go theorem for one-way quantum computing on naturally occurring two-level systems , 2010, 1004.3787.

[67]  Paui Relativistic Field Theories of Elementary Particles ' % , 2011 .

[68]  P. Cai,et al.  Reliable Perturbative Results for Strong Interactions ? , 2011 .

[69]  Ying Ran,et al.  $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: Duality between Schwinger-fermion and Schwinger-boson representations , 2010, 1007.3266.

[70]  Yong Baek Kim,et al.  Topological insulators and metal-insulator transition in the pyrochlore iridates , 2010, 1004.4630.

[71]  Xiao-Gang Wen,et al.  Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order , 2010, 1004.3835.

[72]  Xiao-Liang Qi,et al.  Fractional topological insulators in three dimensions. , 2010, Physical review letters.

[73]  Bei Zeng,et al.  Tensor product representation of a topological ordered phase: Necessary symmetry conditions , 2010, 1003.1774.

[74]  A. Seidel S-duality constraints on 1D patterns associated with fractional quantum Hall states. , 2010, Physical review letters.

[75]  J. Eisert,et al.  Colloquium: Area laws for the entanglement entropy , 2010 .

[76]  X. Wen,et al.  Topological Properties of Tensor Network States From Their Local Gauge and Local Symmetry Structures , 2010, 1001.4517.

[77]  D. Pérez-García,et al.  PEPS as ground states: Degeneracy and topology , 2010, 1001.3807.

[78]  Sergey Bravyi,et al.  Topological quantum order: Stability under local perturbations , 2010, 1001.0344.

[79]  Zhenghan Wang,et al.  Non-Abelian quantum Hall states and their quasiparticles: From the pattern of zeros to vertex algebra , 2009, 0910.3988.

[80]  Frank Pollmann,et al.  Entanglement spectrum of a topological phase in one dimension , 2009, 0910.1811.

[81]  Leon Balents,et al.  Mott physics and band topology in materials with strong spin-orbit interaction , 2009, 0907.2962.

[82]  X. Wen,et al.  Non-Abelian two-component fractional quantum Hall states , 2009, 0906.0356.

[83]  X. Wen,et al.  Classification of Abelian and Non-Abelian Multilayer Fractional Quantum Hall States Through the Pattern of Zeros , 2009, 0906.0337.

[84]  A. Kitaev,et al.  Effects of interactions on the topological classification of free fermion systems , 2009, 0904.2197.

[85]  F. Meier,et al.  A tunable topological insulator in the spin helical Dirac transport regime , 2009, Nature.

[86]  X. Wen,et al.  Translation-symmetry-protected topological orders in quantum spin systems , 2009, 0907.4537.

[87]  Seung-Moon Hong On symmetrization of 6j-symbols and Levin-Wen Hamiltonian , 2009, 0907.2204.

[88]  Z. K. Liu,et al.  Experimental Realization of a Three-Dimensional Topological Insulator , 2010 .

[89]  J. Cardy,et al.  Entanglement entropy and conformal field theory , 2009, 0905.4013.

[90]  R. Roy Topological phases and the quantum spin Hall effect in three dimensions , 2009 .

[91]  Yi Zhang,et al.  Topological insulators in three dimensions from spontaneous symmetry breaking , 2009, 0904.0690.

[92]  Xiao-Gang Wen,et al.  Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order , 2009, 0903.1069.

[93]  Alexei Kitaev,et al.  Periodic table for topological insulators and superconductors , 2009, 0901.2686.

[94]  S. Furukawa,et al.  Mutual information and boson radius in a c=1 critical system in one dimension. , 2008, Physical review letters.

[95]  Xiao-Gang Wen,et al.  Tensor-product representations for string-net condensed states , 2008, 0809.2821.

[96]  M. Aguado,et al.  Explicit tensor network representation for the ground states of string-net models , 2008, 0809.2393.

[97]  X. Wen,et al.  Structure of quasiparticles and their fusion algebra in fractional quantum Hall states , 2008, 0807.2789.

[98]  X. Wen,et al.  Doped kagome system as exotic superconductor , 2008, 0804.1359.

[99]  Andrew W. Cross,et al.  Codeword stabilized quantum codes: Algorithm and structure , 2008, 0803.3232.

[100]  Stephen D Bartlett,et al.  Identifying phases of quantum many-body systems that are universal for quantum computation. , 2008, Physical review letters.

[101]  B. Terhal,et al.  A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes , 2008, 0810.1983.

[102]  Oded Regev,et al.  Quantum SAT for a Qutrit-Cinquit Pair Is QMA1-Complete , 2008, ICALP.

[103]  Hui Li,et al.  Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states. , 2008, Physical review letters.

[104]  A. Seidel Pfaffian statistics through adiabatic transport in the 1D coherent state representation. , 2008, Physical review letters.

[105]  F. Verstraete,et al.  Matrix product operator representations , 2008, 0804.3976.

[106]  D. Sheng,et al.  DMRG Numerical Study of the Kagom\'{e} Antiferromagnet , 2008, 0804.1616.

[107]  D. Hsieh,et al.  A topological Dirac insulator in a quantum spin Hall phase , 2008, Nature.

[108]  M. Kastner,et al.  Quasiparticle Tunneling in the Fractional Quantum Hall State at \nu = 5/2 , 2008, 0803.3530.

[109]  Shinsei Ryu,et al.  Classification of topological insulators and superconductors in three spatial dimensions , 2008, 0803.2786.

[110]  D. L. Zhou,et al.  Irreducible multiparty correlations in quantum states without maximal rank. , 2008, Physical review letters.

[111]  Xiao-Gang Wen,et al.  Mutual Chern-Simons theory for Z 2 topological order , 2008, 0803.2300.

[112]  Ying Ran,et al.  Properties of an algebraic spin liquid on the kagome lattice , 2008, 0803.1150.

[113]  F. Verstraete,et al.  Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , 2008, 0907.2796.

[114]  Xiao-Liang Qi,et al.  Topological field theory of time-reversal invariant insulators , 2008, 0802.3537.

[115]  Zhenghan Wang,et al.  Classification of symmetric polynomials of infinite variables: Construction of Abelian and non-Abelian quantum Hall states , 2008, 0801.3291.

[116]  Kun Yang,et al.  Halperin (m,m',n) bilayer quantum Hall states on thin cylinders. , 2008, Physical review letters.

[117]  Andrew W. Cross,et al.  Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit , 2008, 0801.2360.

[118]  B. Andrei Bernevig,et al.  Generalized clustering conditions of Jack polynomials at negative Jack parameter α , 2007, 0711.3062.

[119]  Xiao-Liang Qi,et al.  Topological Mott insulators. , 2007, Physical review letters.

[120]  Andrew W. Cross,et al.  Codeword stabilized quantum codes , 2008, 2008 IEEE International Symposium on Information Theory.

[121]  B Andrei Bernevig,et al.  Model fractional quantum Hall states and Jack polynomials. , 2007, Physical review letters.

[122]  Frank Verstraete,et al.  Peps as unique ground states of local hamiltonians , 2007, Quantum Inf. Comput..

[123]  Norbert Schuch,et al.  Entropy scaling and simulability by matrix product states. , 2007, Physical review letters.

[124]  Samuel L. Braunstein,et al.  ε-convertibility of entangled states and extension of Schmidt rank in infinite-dimensional systems , 2008, Quantum Inf. Comput..

[125]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[126]  Ying Ran,et al.  Spontaneous parity breaking and spin ordering of Dirac spin liquid in a magnetic field , 2007 .

[127]  L. Molenkamp,et al.  Quantum Spin Hall Insulator State in HgTe Quantum Wells , 2007, Science.

[128]  Sandy Irani,et al.  The Power of Quantum Systems on a Line , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[129]  M. Hastings,et al.  An area law for one-dimensional quantum systems , 2007, 0705.2024.

[130]  Zohar Nussinov,et al.  A symmetry principle for topological quantum order , 2007, cond-mat/0702377.

[131]  Michael Levin,et al.  Tensor renormalization group approach to two-dimensional classical lattice models. , 2006, Physical review letters.

[132]  Dung-Hai Lee,et al.  Domain-wall-type defects as anyons in phase space , 2006, cond-mat/0611535.

[133]  Ying Ran,et al.  Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice. , 2006, Physical review letters.

[134]  D. Gross,et al.  Novel schemes for measurement-based quantum computation. , 2006, Physical review letters.

[135]  Liang Fu,et al.  Topological insulators in three dimensions. , 2006, Physical review letters.

[136]  J. E. Moore,et al.  Topological invariants of time-reversal-invariant band structures , 2006, cond-mat/0607314.

[137]  G. Vidal Entanglement renormalization. , 2005, Physical review letters.

[138]  Shou-Cheng Zhang,et al.  Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells , 2006, Science.

[139]  M. Freedman,et al.  From String Nets to Nonabelions , 2006, cond-mat/0610583.

[140]  S. Furukawa,et al.  Reduced density matrices and topological order in a quantum dimer model , 2006, cond-mat/0607050.

[141]  F. Verstraete,et al.  Criticality, the area law, and the computational power of projected entangled pair states. , 2006, Physical review letters.

[142]  Dung-Hai Lee,et al.  Abelian and non-abelian Hall liquids and charge-density wave: quantum number fractionalization in one and two dimensions. , 2006, Physical review letters.

[143]  E. Bergholtz,et al.  Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus , 2006, cond-mat/0604251.

[144]  F. Verstraete,et al.  Lieb-Robinson bounds and the generation of correlations and topological quantum order. , 2006, Physical review letters.

[145]  Sergey Bravyi,et al.  Efficient algorithm for a quantum analogue of 2-SAT , 2006, quant-ph/0602108.

[146]  N. Read Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere , 2006, cond-mat/0601678.

[147]  G. Vidal,et al.  Classical simulation of quantum many-body systems with a tree tensor network , 2005, quant-ph/0511070.

[148]  Xiao-Gang Wen,et al.  Detecting topological order in a ground state wave function. , 2005, Physical review letters.

[149]  J. Preskill,et al.  Topological entanglement entropy. , 2005, Physical review letters.

[150]  S. Furukawa,et al.  Systematic derivation of order parameters through reduced density matrices. , 2005, Physical review letters.

[151]  Michael Levin,et al.  Quantum ether: photons and electrons from a rotor model , 2005, hep-th/0507118.

[152]  Shou-Cheng Zhang,et al.  Quantum spin Hall effect. , 2005, Physical review letters.

[153]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[154]  Andreas Winter,et al.  Partial quantum information , 2005, Nature.

[155]  G. Moore,et al.  Classification of abelian spin Chern-Simons theories , 2005, hep-th/0505235.

[156]  M. Hastings,et al.  Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance , 2005, cond-mat/0503554.

[157]  C. Kane,et al.  Quantum spin Hall effect in graphene. , 2004, Physical review letters.

[158]  J I Cirac,et al.  Renormalization-group transformations on quantum states. , 2004, Physical review letters.

[159]  P. Goldbart,et al.  Global entanglement and quantum criticality in spin chains , 2004, quant-ph/0405162.

[160]  Michael Levin,et al.  String-net condensation: A physical mechanism for topological phases , 2004, cond-mat/0404617.

[161]  E. Schrödinger Die gegenwärtige Situation in der Quantenmechanik , 2005, Naturwissenschaften.

[162]  Michael Levin,et al.  2 3 Se p 20 05 Photons and electrons as emergent phenomena , 2005 .

[163]  C. Gardiner,et al.  Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics , 2004 .

[164]  F. Verstraete,et al.  Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions , 2004, cond-mat/0407066.

[165]  S. Sondhi,et al.  Superconductors are topologically ordered , 2004, cond-mat/0404327.

[166]  F. Verstraete,et al.  Valence-bond states for quantum computation , 2003, quant-ph/0311130.

[167]  M. Hastings Lieb-Schultz-Mattis in higher dimensions , 2003, cond-mat/0305505.

[168]  M. Fisher,et al.  Pyrochlore photons: The U ( 1 ) spin liquid in a S = 1 2 three-dimensional frustrated magnet , 2003, cond-mat/0305401.

[169]  A. Winter,et al.  Communications in Mathematical Physics Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality , 2022 .

[170]  R. Moessner,et al.  Three-dimensional resonating-valence-bond liquids and their excitations , 2003, cond-mat/0307592.

[171]  Michael J. Berry,et al.  Network information and connected correlations. , 2003, Physical review letters.

[172]  X. Wen Quantum order from string net condensations and origin of light and massless fermions , 2003, hep-th/0302201.

[173]  Michael Levin,et al.  Fermions, strings, and gauge fields in lattice spin models , 2003, cond-mat/0302460.

[174]  G. Vidal,et al.  Entanglement in quantum critical phenomena. , 2002, Physical review letters.

[175]  X. Wen Artificial light and quantum order in systems of screened dipoles , 2002, cond-mat/0210040.

[176]  X. Wen Quantum orders in an exact soluble model. , 2002, Physical review letters.

[177]  A. Kitaev,et al.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[178]  G. Hooft Confinement of quarks , 2003 .

[179]  W. Wootters,et al.  Almost every pure state of three qubits is completely determined by its two-particle reduced density matrices. , 2002, Physical review letters.

[180]  O. Motrunich,et al.  Exotic order in simple models of bosonic systems. , 2002, Physical review letters.

[181]  O. Motrunich,et al.  Microscopic models for fractionalized phases in strongly correlated systems , 2002, cond-mat/0201320.

[182]  X. Wen Origin of gauge bosons from strong quantum correlations. , 2001, Physical review letters.

[183]  P. Parrilo,et al.  Distinguishing separable and entangled states. , 2001, Physical review letters.

[184]  D. Schlingemann Stabilizer codes can be realized as graph codes , 2001, Quantum Inf. Comput..

[185]  J. Preskill,et al.  Topological quantum memory , 2001, quant-ph/0110143.

[186]  X. Wen Quantum orders and symmetric spin liquids , 2001, cond-mat/0107071.

[187]  X. Wen Quantum order: a quantum entanglement of many particles , 2001, cond-mat/0110397.

[188]  Shun-ichi Amari,et al.  Information geometry on hierarchy of probability distributions , 2001, IEEE Trans. Inf. Theory.

[189]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[190]  A. Gendiar,et al.  Two-Dimensional Tensor Product Variational Formulation , 2000, cond-mat/0011103.

[191]  R. Moessner,et al.  Resonating valence bond phase in the triangular lattice quantum dimer model. , 2000, Physical review letters.

[192]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[193]  X. G. Wen Ground state degeneracy of the FQH states in presence of random potential and on high genus Riemann surfaces † , 2001 .

[194]  Dirk Schlingemann,et al.  Quantum error-correcting codes associated with graphs , 2000, ArXiv.

[195]  P. Marchetti,et al.  Spin-statistics transmutation in relativistic quantum field theories of dyons , 2000, hep-th/0010291.

[196]  A. Kitaev Unpaired Majorana fermions in quantum wires , 2000, cond-mat/0010440.

[197]  Charles H. Bennett,et al.  Exact and asymptotic measures of multipartite pure-state entanglement , 1999, Physical Review A.

[198]  N. Read,et al.  Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect , 1999, cond-mat/9906453.

[199]  泰啓 日永田 Numerical renormalization approach to two-dimensional quantum antiferromagnets with valence-bond-solid type ground state , 1999 .

[200]  William M. Steen,et al.  Atom-Photon Interactions Basic Processes and Applications , 1992 .

[201]  C. Lhuillier,et al.  Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice , 1998, cond-mat/9812329.

[202]  M. Martin-Delgado,et al.  The Density Matrix Renormalization Group, Quantum Groups and Conformal Field Theory , 1998, cond-mat/9811170.

[203]  T. Nishino,et al.  A Density Matrix Algorithm for 3D Classical Models , 1998, cond-mat/9804134.

[204]  John Preskill,et al.  Topological Quantum Computation , 1998, QCQC.

[205]  T. Nishino,et al.  Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains , 1997, cond-mat/9710310.

[206]  A. Kitaev Quantum computations: algorithms and error correction , 1997 .

[207]  S. Cheluvaraja Phase transitions in Abelian lattice gauge theories , 1997, hep-lat/9705041.

[208]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.

[209]  J. Zittartz,et al.  Quantum phase transition in spin-3/2 systems on the hexagonal lattice — optimum ground state approach , 1997, cond-mat/9702178.

[210]  N. Sloane,et al.  Quantum error correction via codes over GF(4) , 1996, Proceedings of IEEE International Symposium on Information Theory.

[211]  E. Knill,et al.  Theory of quantum error-correcting codes , 1996, quant-ph/9604034.

[212]  A. Zee,et al.  Topological Degeneracy of Quantum Hall Fluids , 1997 .

[213]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[214]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[215]  A. Steane Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[216]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[217]  Östlund,et al.  Thermodynamic limit of density matrix renormalization. , 1995, Physical review letters.

[218]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[219]  Lloyd,et al.  Almost any quantum logic gate is universal. , 1995, Physical review letters.

[220]  D. Deutsch,et al.  Universality in quantum computation , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[221]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[222]  DiVincenzo,et al.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[223]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[224]  Ng Edge states in antiferromagnetic quantum spin chains. , 1994, Physical review. B, Condensed matter.

[225]  F. Wilczek,et al.  Geometric and renormalized entropy in conformal field theory , 1994, hep-th/9403108.

[226]  Bruno Nachtergaele,et al.  Finitely Correlated Pure States , 1994 .

[227]  X. Wen,et al.  The Ground state structure and modular transformations of fractional quantum Hall states on a torus , 1993, hep-th/9303155.

[228]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[229]  M. Fannes,et al.  Finitely correlated states on quantum spin chains , 1992 .

[230]  Kennedy,et al.  Hidden Z2 x Z2 symmetry breaking in Haldane-gap antiferromagnets. , 1992, Physical review. B, Condensed matter.

[231]  Lee,et al.  Observation of fractional spin S=1/2 on open ends of S=1 linear antiferromagnetic chains: Nonmagnetic doping. , 1991, Physical review letters.

[232]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[233]  Wen,et al.  Mean-field theory of spin-liquid states with finite energy gap and topological orders. , 1991, Physical review. B, Condensed matter.

[234]  X. Wen Topological Orders and Chern-Simons Theory in Strongly Correlated Quantum Liquid , 1991 .

[235]  Read,et al.  Large-N expansion for frustrated quantum antiferromagnets. , 1991, Physical review letters.

[236]  Wen Non-Abelian statistics in the fractional quantum Hall states. , 1991, Physical review letters.

[237]  Hagiwara,et al.  Observation of S=1/2 degrees of freedom in an S=1 linear-chain Heisenberg antiferromagnet. , 1990, Physical review letters.

[238]  Wen,et al.  Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces. , 1990, Physical review. B, Condensed matter.

[239]  A. Zeilinger,et al.  Going Beyond Bell’s Theorem , 2007, 0712.0921.

[240]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[241]  Wen,et al.  Vacuum degeneracy of chiral spin states in compactified space. , 1989, Physical review. B, Condensed matter.

[242]  D. Deutsch Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[243]  M. Nijs,et al.  Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains. , 1989, Physical review. B, Condensed matter.

[244]  Edward Witten,et al.  Quantum field theory and the Jones polynomial , 1989 .

[245]  Zee,et al.  Chiral spin states and superconductivity. , 1989, Physical review. B, Condensed matter.

[246]  Zhang,et al.  Effective-field-theory model for the fractional quantum Hall effect. , 1989, Physical review letters.

[247]  E. Lieb,et al.  Valence bond ground states in isotropic quantum antiferromagnets , 1988 .

[248]  I. Affleck,et al.  Large-n limit of the Heisenberg-Hubbard model: Implications for high-Tc superconductors. , 1988, Physical review. B, Condensed matter.

[249]  P. Anderson,et al.  Gauge theory of high-temperature superconductors and strongly correlated Fermi systems. , 1988, Physical review. B, Condensed matter.

[250]  R. Laughlin,et al.  Equivalence of the resonating-valence-bond and fractional quantum Hall states. , 1987, Physical review letters.

[251]  Kennedy,et al.  Rigorous results on valence-bond ground states in antiferromagnets. , 1987, Physical review letters.

[252]  Macdonald,et al.  Off-diagonal long-range order, oblique confinement, and the fractional quantum Hall effect. , 1987, Physical review letters.

[253]  Haldane,et al.  Periodic Laughlin-Jastrow wave functions for the fractional quantized Hall effect. , 1985, Physical review. B, Condensed matter.

[254]  Frank Wilczek,et al.  Fractional Statistics and the Quantum Hall Effect , 1984 .

[255]  Frank Wilczek,et al.  Appearance of Gauge Structure in Simple Dynamical Systems , 1984 .

[256]  B. Halperin Statistics of quasiparticles and the hierarchy of fractional quantized Hall states , 1984 .

[257]  R. Laughlin Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations , 1983 .

[258]  F. Haldane Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model , 1983 .

[259]  O. Klein Quantum Theory and 5-DIMENSIONAL Theory of Relativity , 1983 .

[260]  R. Feynman Simulating physics with computers , 1999 .

[261]  Frank Wilczek,et al.  Quantum Mechanics of Fractional-Spin Particles , 1982 .

[262]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[263]  A. Goldhaber Electromagnetism, Spin, and Statistics , 1982 .

[264]  D. C. Tsui,et al.  Two-Dimensional Magnetotransport in the Extreme Quantum Limit , 1982 .

[265]  F. Wilczek Remarks on Dyons , 1982 .

[266]  B. Halperin Quantized Hall conductance, current carrying edge states, and the existence of extended states in a two-dimensional disordered potential , 1982 .

[267]  G. Dorda,et al.  New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance , 1980 .

[268]  H. Nielsen,et al.  Dynamical stability of local gauge symmetry Creation of light from chaos , 1980 .

[269]  Robert Savit,et al.  Duality in field theory and statistical systems , 1980 .

[270]  John B. Kogut,et al.  An introduction to lattice gauge theory and spin systems , 1979 .

[271]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[272]  J. Myrheim,et al.  On the theory of identical particles , 1977 .

[273]  R. Hudson,et al.  Locally normal symmetric states and an analogue of de Finetti's theorem , 1976 .

[274]  Claudio Rebbi,et al.  Solitons with Fermion Number 1/2 , 1976 .

[275]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[276]  C. Rebbi,et al.  Spin from Isospin in a Gauge Theory , 1976 .

[277]  J. Kogut,et al.  Hamiltonian Formulation of Wilson's Lattice Gauge Theories , 1975 .

[278]  F. Wilczek,et al.  Ultraviolet Behavior of Non-Abelian Gauge Theories , 1973 .

[279]  D. W. Robinson,et al.  The finite group velocity of quantum spin systems , 1972 .

[280]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[281]  A. J. Coleman THE STRUCTURE OF FERMION DENSITY MATRICES , 1963 .

[282]  Chen Ning Yang,et al.  Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors , 1962 .

[283]  E. Lieb,et al.  Two Soluble Models of an Antiferromagnetic Chain , 1961 .

[284]  H. Trotter On the product of semi-groups of operators , 1959 .

[285]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[286]  D. D. Hoppes,et al.  Experimental Test of Parity Conservation in Beta Decay , 1957 .

[287]  Chen Ning Yang,et al.  Question of Parity Conservation in Weak Interactions , 1956 .

[288]  R. L. Mills,et al.  Conservation of Isotopic Spin and Isotopic Gauge Invariance , 1954 .

[289]  K. Cheng Theory of Superconductivity , 1948, Nature.

[290]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[291]  E. Fermi,et al.  Zur Quantelung des idealen einatomigen Gases , 1926 .

[292]  Paul Adrien Maurice Dirac,et al.  On the Theory of quantum mechanics , 1926 .

[293]  Theodor Kaluza On the Problem of Unity in Physics , 1921 .

[294]  A. Einstein The Foundation of the General Theory of Relativity , 1916 .

[295]  A. Einstein On the Electrodynamics of Moving Bodies , 2005 .

[296]  X. Wen Topological Orders in Rigid States * , 2022 .