Quantum Error Correction and Orthogonal Geometry

Calderbank, A. R., Rains, E. M., Shor, P. W., Sloane, N. J. A.·1997·Physical Review Letters

Cited by (790)

Items 101–200 of 790

  1. Mutually unbiased measurements in finite dimensions
    Amir Kalev, Gilad Gour · 2014 · New Journal of Physics
  2. Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
    Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto, Diego Ruano · 2019 · Quantum Information Processing
  3. Environment-Induced Decoherence and the Transition from Quantum to Classical
    Juan Pablo Paz, Wojciech Hubert Zurek · 2007 · Springer eBooks
  4. Commuting Pauli Hamiltonians as maps between free modules
    Jeongwan Haah · 2012
  5. Optimum quantum error recovery using semidefinite programming
    Andrew S. Fletcher, Peter W. Shor, Moe Z. Win · 2007 · Physical Review A
  6. Topics in Quantum Computers
    David Peter Divincenzo · 1997 · Springer eBooks
  7. A Nonadditive Quantum Code
    Eric M. Rains, Ronald H. Hardin, Peter W. Shor, Neil J.A. Sloane · 1997 · Physical Review Letters
  8. Group representations, error bases and quantum codes
    NM (United States) Los Alamos National Lab., Emanuel H. Knill, USDOE, Washington, DC (United States) · 1996
  9. Basic Concepts in Quantum Computation
    ARTUR K. EKERT, Patrick M. Hayden, Hitoshi Inamori · 2007 · Springer eBooks
  10. Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
    Armin Tavakoli, Máté Farkas, Denis Rosset, Jean-Daniel Bancal, Jędrzej Kaniewski · 2021 · Science Advances
  11. Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies
    Alexey E. Rastegin · 2013 · The European Physical Journal D
  12. Efficient Quantum Transforms
    Peter Høyer · 1997 · arXiv (Cornell University)
  13. Early Fault-Tolerant Quantum Computing
    Katabarwa, Amara, Gratsea, Katerina, Caesura, Athena, Johnson, Peter D. · 2024 · PRX Quantum
  14. The Invariants of the Clifford Groups
    Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane · 2001 · Designs Codes and Cryptography
  15. Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators
    Ching–Yi Lai, Alexei Ashikhmin · 2017 · IEEE Transactions on Information Theory
  16. Convolutional and Tail-Biting Quantum Error-Correcting Codes
    G. David Forney, Markus Grassl, Saikat Guha · 2007 · IEEE Transactions on Information Theory
  17. Qubit devices and the issue of quantum decoherence
    Howard E. Brandt · 1999 · Progress in Quantum Electronics
  18. Constructions of new families of nonbinary quantum codes
    Giuliano G. La Guardia · 2009 · Physical Review A
  19. Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes
    Theodore J. Yoder, Ryuji Takagi, Isaac L. Chuang · 2016 · Physical Review X
  20. No-Go Theorems for Quantum Resource Purification
    Kun Fang, Zi-Wen Liu · 2020 · Physical Review Letters
  21. Structure of the sets of mutually unbiased bases for N qubits
    José Luis Romero, Gunnar G. Bjork, A. B. Klimov, Luis Lorenzo Sánchez-Soto · 2005 · Physical Review A
  22. Quantum generalized Reed-Solomon codes: Unified framework for quantum maximum-distance-separable codes
    Zhuo Li, Lijuan Xing, Xinmei Wang · 2008 · Physical Review A
  23. Asymptotically good quantum codes
    Alexei Ashikhmin, Simon N. Litsyn, Michael Anatol'evich Tsfasman · 2001 · Physical Review A
  24. Entanglement increases the error-correcting ability of quantum error-correcting codes
    Ching–Yi Lai, Todd A. Brun · 2013 · Physical Review A
  25. About mutually unbiased bases in even and odd prime power dimensions
    Thomas Durt · 2005 · Journal of Physics A Mathematical and General
  26. Hardness of Decoding Quantum Stabilizer Codes
    Pavithran Sridharan Iyer, David Poulin · 2015 · IEEE Transactions on Information Theory
  27. An Introduction to Quantum Error Correction
    Daniel Gottesman · 2000 · arXiv (Cornell University)
  28. Quantum Error Correction
    Ivan B. Djordjević · 2012 · Elsevier eBooks
  29. Environment-Induced Decoherence and the Transition from Quantum to Classical
    J. P. Paz, W. H. Zurek · 2007 · Springer eBooks
  30. Advantages of versatile neural-network decoding for topological codes
    Nishad Maskara, Aleksander Kubica, Tomas Jochym-O’Connor · 2019 · Physical Review A
  31. Codes and Protocols for Distilling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> , controlled- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> , and Toffoli Gates
    Haah, Jeongwan, Hastings, Matthew B. · 2018 · Quantum
  32. Achievable rates for the Gaussian quantum channel
    Jim Harrington, John P. Preskill · 2001 · Physical Review A
  33. Self-correcting quantum computers
    Héctor Bombín, Ravindra W. Chhajlany, Michał Horodecki, Miguel Angel Martin-Delgado · 2013 · New Journal of Physics
  34. Duality in Entanglement-Assisted Quantum Error Correction
    Ching–Yi Lai, Todd A. Brun, Mark M. Wilde · 2013 · IEEE Transactions on Information Theory
  35. Quantum error correcting codes from the compression formalism
    Man-Duen Choi, David W. Kribs, Karol Życzkowski · 2006 · Reports on Mathematical Physics
  36. Quantifying Measurement Incompatibility of Mutually Unbiased Bases
    Sébastien Designolle, Paul Skrzypczyk, Florian Fröwis, Nicolas Brunner · 2019 · Physical Review Letters
  37. Nontrivial Quantum Cellular Automata in Higher Dimensions
    Jeongwan Haah, Lukasz Fidkowski, Matthew B. Hastings · 2022 · Communications in Mathematical Physics
  38. Introduction to Quantum Error Correction
    Emanuel H. Knill, Raymond Laflamme, Alexei Ashikhmin, Howard Barnum, Lorenza Viola, Wojciech Hubert Zurek · 2002 · arXiv (Cornell University)
  39. A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
    A.R. Calderbank, Ronald H. Hardin, Eric M. Rains, Peter W. Shor, Neil J.A. Sloane · 1999 · Journal of Algebraic Combinatorics
  40. Commutative version of the local Hamiltonian problem and common eigenspace problem
    Sergey B. Bravyi, M. Vyalyi · 2005 · Quantum Information and Computation
  41. Graphical nonbinary quantum error-correcting codes
    Dan Mei Hu, Weidong Tang, Meisheng Zhao, Qing Chen, Sixia Yu, C. H. Oh · 2008 · Physical Review A
  42. Quantum code words contradict local realism
    David Peter Divincenzo, Asher Peres · 1997 · Physical Review A
  43. Upper bounds on the size of quantum codes
    Alexei Ashikhmin, S. Litsyu · 1999 · IEEE Transactions on Information Theory
  44. Shorter Stabilizer Circuits via Bruhat Decomposition and Quantum Circuit Transformations
    Dmitri Maslov, Martin Roetteler · 2018 · IEEE Transactions on Information Theory
  45. Binary LCD Codes and Self-Orthogonal Codes From a Generic Construction
    Zhengchun Zhou, Xia Li, Chunming Tang, Cunsheng Ding · 2018 · IEEE Transactions on Information Theory
  46. Multipulse control of decoherence
    Chikako Uchiyama, Masaki Aihara · 2002 · Physical Review A
  47. The Hidden Subgroup Problem - Review and Open Problems
    Chris Lomont · 2004 · arXiv (Cornell University)
  48. Fault-Tolerant Holonomic Quantum Computation
    Ognyan Oreshkov, Todd A. Brun, Daniel A. Lidar · 2009 · Physical Review Letters
  49. Magic state distillation with low space overhead and optimal asymptotic input count
    Jeongwan Haah, Matthew B. Hastings, David Poulin, D. Wecker · 2017 · Quantum
  50. Structure of 2D Topological Stabilizer Codes
    Héctor Bombín · 2014 · Communications in Mathematical Physics
  51. On binary constructions of quantum codes
    Gérard Cohen, S. Encheva, Simon N. Litsyn · 1999 · IEEE Transactions on Information Theory
  52. Topological Protection and Quantum Noiseless Subsystems
    Paolo Zanardi A, Seth Lloyd · 2003 · Physical Review Letters
  53. The art of signaling: fifty years of coding theory
    A.R. Calderbank · 1998 · IEEE Transactions on Information Theory
  54. Preparing encoded states in an oscillator
    B. C. Travaglione, Gerard J Milburn · 2002 · Physical Review A
  55. Prevention of dissipation with two particles
    L.-M. Duan, Guang‐Can Guo · 1998 · Physical Review A
  56. Quantum convolutional codes: fundamentals
    Ollivier, H., Jean–Pierre Tillich · 2004 · arXiv (Cornell University)
  57. Quantum error correction against correlated noise
    James Clemens, Shabnam Siddiqui, Julio R. Gea-Banacloche · 2004 · Physical Review A
  58. Quantum error correction with the semion code
    Guillaume Dauphinais, Laura Ortíz, Santiago Varona, Miguel Angel Martin-Delgado · 2019 · New Journal of Physics
  59. Quantum MDS codes with large minimum distance
    Tao Zhang, Gennian Ge · 2016 · Designs Codes and Cryptography
  60. Supersinglets
    Adán Cabello · 2003 · Journal of Modern Optics
  61. Optimal quantum codes for preventing collective amplitude damping
    L.-M. Duan, Guang‐Can Guo · 1998 · Physical Review A
  62. Entanglement-assisted quantum convolutional coding
    Mark M. Wilde, Todd A. Brun · 2010 · Physical Review A
  63. Entanglement-assisted quantum error-correcting codes with imperfect ebits
    Ching–Yi Lai, Todd A. Brun · 2012 · Physical Review A
  64. Continuous error correction
    Juan Pablo Paz, Wojciech Hubert Zurek · 1998 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
  65. Chapter 7 The discrete Wigner function
    Gunnar G. Bjork, A. B. Klimov, Luis Lorenzo Sánchez-Soto · 2008 · Progress in optics
  66. Квантовые вычисления: алгоритмы и исправление ошибок
    Алексей Юрьевич Китаев, Aleksei Yur'evich Kitaev · 1997 · Успехи математических наук
  67. Preserving Quantum States using Inverting Pulses: A Super-Zeno Effect
    Deepak Dhar, Lov K. Grover, Shasanka Mohan Roy · 2006 · Physical Review Letters
  68. Real Randomized Benchmarking
    A. K. Hashagen, Steven T. Flammia, D. Gross, Joel J. Wallman · 2018 · Quantum
  69. Algebraic Methods for Quantum Codes on Lattices
    Jeongwan Haah · 2017 · Revista Colombiana de Matemáticas
  70. Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping
    Aleksander Kubica, Michael E. Beverland, Fernando G. S. L. Brandão, John P. Preskill, Krysta M. Svore · 2018 · Physical Review Letters
  71. Universal fault-tolerant measurement-based quantum computation
    Benjamin J. Brown, Sam Roberts · 2020 · Physical Review Research
  72. Quantum stabilizer codes, lattices, and CFTs
    Anatoly Y. Dymarsky, Alfred D. Shapere · 2021 · Journal of High Energy Physics
  73. Nonadiabatic geometrical quantum gates in semiconductor quantum dots
    Paolo Solinas, Paolo Zanardi A, Nino Zanghı̀, Fausto Rossi · 2003 · Physical Review A
  74. Decoherence slowing down in a symmetry-broken environment
    Simone Paganelli, FERDINANDO DE PASQUALE, S. M. Giampaolo · 2002 · Physical Review A
  75. Geometrical approach to mutually unbiased bases
    Andrei B Klimov, José L Romero, Gunnar G. Bjork, Luis Lorenzo Sánchez-Soto · 2007 · Journal of Physics A Mathematical and Theoretical
  76. Constructions of new families of nonbinary CSS codes
    Giuliano G. La Guardia, Reginaldo Palazzo · 2010 · Discrete Mathematics
  77. Subsystem codes with spatially local generators
    Sergey B. Bravyi · 2011 · Physical Review A
  78. Permutationally invariant codes for quantum error correction
    Harriet Pollatsek, Mary Beth Ruskai · 2004 · Linear Algebra and its Applications
  79. Resonant cancellation of off-resonant effects in a multilevel qubit
    Lin Tian, Seth Lloyd · 2000 · Physical Review A
  80. Analysis of Quantum Error-Correcting Codes: Symplectic Lattice Codes and Toric Codes
    James William Harrington · 2004 · CaltechTHESIS (California Institute of Technology)
  81. Photon-number entangled states generated in Kerr media with optical parametric pumping
    A. Kowalewska-Kudłaszyk, W. Leoński, Jan Peřina · 2011 · Physical Review A
  82. Nonadditive Quantum Error-Correcting Code
    Sixia Yu, Qing Chen, Ching–Yi Lai, C. H. Oh · 2008 · Physical Review Letters
  83. A Survey on Available Tools and Technologies Enabling Quantum Computing
    Prateek Singh, R. Dasgupta, Anushka Singh, Harsh Pandey, Vikas Hassija, Vinay Chamola, Biplab Sikdar · 2024 · IEEE Access
  84. Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D
    Jeongwan Haah · 2021 · Journal of Mathematical Physics
  85. Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
    Mitsuru Hamada · 2008 · IEEE Transactions on Information Theory
  86. Efficient color code decoders in d ≥ 2 dimensions from toric code decoders
    Aleksander Kubica, Nicolas Delfosse · 2023 · Quantum
  87. Pseudo-randomness and Learning in Quantum Computation
    Richard A. Low · 2010 · arXiv (Cornell University)
  88. Catalysis in quantum information theory
    Patryk Lipka-Bartosik, Henrik Wilming, Nelly H. Y. Ng · 2024 · Reviews of Modern Physics
  89. Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions
    Peiyu Tan, Jing Li · 2010 · IEEE Transactions on Information Theory
  90. MDS Codes With Galois Hulls of Arbitrary Dimensions and the Related Entanglement-Assisted Quantum Error Correction
    Meng Cao · 2021 · IEEE Transactions on Information Theory
  91. Quantum error detection .I. Statement of the problem
    Alexei Ashikhmin, Alexander Barg, Emanuel H. Knill, Simon N. Litsyn · 2000 · IEEE Transactions on Information Theory
  92. Minimal qudit code for a qubit in the phase-damping channel
    Stefano Pirandola, Stefano Mancini, Samuel L. Braunstein, David Vitali · 2008 · Physical Review A
  93. Quasi-cyclic constructions of quantum codes
    Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto · 2018 · Finite Fields and Their Applications
  94. Algebraic and information-theoretic conditions for operator quantum error correction
    Michael A. Nielsen, David Poulin · 2007 · Physical Review A
  95. Pauli Exchange Errors in Quantum Computation
    Mary Beth Ruskai · 2000 · Physical Review Letters
  96. Quantum error correction may delay, but also cause, entanglement sudden death
    Isabel Sainz, Gunnar G. Bjork · 2008 · Physical Review A
  97. Decoherence of molecular vibrational wave packets: Observable manifestations and control criteria
    Constantin Brif, HERSCHEL A. RABITZ, Sascha Wallentowitz, Ian A. Walmsley · 2001 · Physical Review A
  98. Prospects and challenges of quantum finance
    Bouland, Adam, van Dam, Wim, Joorati, Hamed, Kerenidis, Iordanis, Prakash, Anupam · 2020 · arXiv
  99. Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes
    Yang Liu, Ruihu Li, Liangdong Lv, Yuena Ma · 2018 · Quantum Information Processing
  100. MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES
    Robert Raussendorf · 2009 · International Journal of Quantum Information