@article{Aaronson04, author = {Scott Aaronson and Daniel Gottesman}, title = {Improved simulation of stabilizer circuits}, year = {2004}, journal = {Phys. Rev. A}, volume = {70}, number = {5}, numpages = {14}, pages = {052328}, keywords = {quantum gates; algorithm theory}, eprint = {arXiv:quant-ph/0406196} } @inproceedings{Aharonov97, author = {Dorit Aharonov and Michael Ben-Or}, title = {Fault tolerant quantum computation with constant error}, booktitle = {Proc. ACM STOC}, pages = {176--188}, year = {1997}, eprint = {arXiv:quant-ph/9611025}, } @MISC{Aharonov99, author = {Dorit Aharonov and Michael Ben-Or}, title = {Fault-Tolerant Quantum Computation With Constant Error Rate}, year = {1999}, eprint = {arXiv:quant-ph/9906129}, notes = {Expanded version of Aharonov97.} } @inproceedings{Aharonov06, author = {Dorit Aharonov and Vaughan Jones and Zeph Landau}, title = {A polynomial quantum algorithm for approximating the Jones polynomial}, booktitle = {Proc. 38th Symp. Theory Comp.}, pages = {427}, year = {2006}, eprint = {arXiv:quant-ph/0511096}, notes = {This was the debut of an explicit algorithm for approximating the Jones polynomial.} } @ARTICLE{Aharonov08, author = {Dorit Aharonov and Vaughan Jones and Zeph Landau}, title = {A Polynomial Quantum Algorithm for Approximating the Jones Polynomial}, journal = {Algorithmica (Online)}, eprint = {arXiv:quant-ph/0511096}, year = {2008} notes = {Expanded version of Aharonov06.} } @ARTICLE{Aliferis06, author = {Panos Aliferis and Daniel Gottesman and John Preskill}, title = {Quantum accuracy threshold for concatenated distance-3 codes}, journal = {Quantum Information and Computation}, volume = {6}, pages = {97--165}, year = {2006}, eprint = {arXiv:quant-ph/0504218}, } @ARTICLE{Aliferis07, author = {Panos Aliferis and Barbara M. Terhal}, title = {Fault-Tolerant Quantum Computation for Local Leakage Faults}, journal = {Quantum Information and Computation}, volume = {7}, pages = {139--156}, year = {2007}, eprint = {arXiv:quant-ph/0511065}, } @article{Aliferis07b, author = {Panos Aliferis and Andrew W. Cross}, title = {Subsystem Fault Tolerance with the Bacon-Shor Code}, year = {2007}, journal = {Phys. Rev. Lett.}, volume = {98}, number = {22}, eid = {220502}, numpages = {4}, pages = {220502}, eprint = {arXiv:quant-ph/0610063} } @article{Bacon06, author = {Dave Bacon}, title = {Operator quantum error-correcting subsystems for self-correcting quantum memories}, year = {2006}, journal = {Phys. Rev. A}, volume = {73}, number = {1}, eid = {012340}, pages = {012340}, keywords = {quantum computing; error correction; encoding; Hilbert spaces}, eprint = {arXiv:quant-ph/0506023}, } @Article{Barenco95, title = {Elementary gates for quantum computation}, author = {Adriano Barenco and Charles H. Bennett and Richard Cleve and David P. DiVincenzo and Norman Margolus and Peter Shor and Tycho Sleator and John A. Smolin and Harald Weinfurter}, journal = {Phys. Rev. A}, volume = {52}, number = {5}, pages = {3457--3467}, numpages = {10}, year = {1995}, month = {Nov}, eprint = {arXiv:quant-ph/9503016}, notes = {Shows how to construct arbitrary two-state level transitions.} } @article{Barrett07, author = {Jonathan Barrett and Carlton M. Caves and Bryan Eastin and Matthew B. Elliott and Stefano Pironio}, title = {Modeling Pauli measurements on graph states with nearest-neighbor classical communication}, year = {2007}, journal = {Phys. Rev. A}, volume = {75}, number = {1}, eid = {012103}, numpages = {8}, pages = {012103}, eprint = {arXiv:quant-ph/0603032}, keywords = {quantum theory; quantum communication; information theory; protocols; mathematical operators; graph theory} } @article{Bell64, author = {John S. Bell}, title = {On the {E}instein-{P}odolsky-{R}osen paradox}, journal = {Physics}, volume = {1}, pages = {195-200}, year = {1964} } @inproceedings{Boykin99, author = {P. O. Boykin and T. Mor and M. Pulver and V. Roychowdhury and F. Vatan}, title = {On universal and fault-tolerant quantum computing: a novel basis and a new constructive proof of universality for {S}hor's basis}, booktitle = {FOCS 1999: 40th Annual IEEE Symposium on Foundations of Computer Science}, month = {October}, year = {1999}, address = {New York, NY}, pages = {486-494}, eprint = {arXiv:quant-ph/9906054}, notes = {Explains how to generate an arbitrary single-qubit rotation using H, CX, and T.} } @article{Bravyi05, author = {Sergey Bravyi and Alexei Kitaev}, title = {Universal quantum computation with ideal Clifford gates and noisy ancillas}, publisher = {APS}, year = {2005}, journal = {Phys. Rev. A}, volume = {71}, number = {2}, eid = {022316}, pages = {022316}, keywords = {quantum computing; protocols; error analysis}, doi = {10.1103/PhysRevA.71.022316}, eprint = {arXiv:quant-ph/0403025} } @inproceedings{Buhrman06, author = {Harry Buhrman and Richard Cleve and Monique Laurent and Noah Linden and Alexander Schrijver and Falk Unger}, title = {New Limits on Fault-Tolerant Quantum Computation}, booktitle = {FOCS 2006: 47th Annual IEEE Symposium on Foundations of Computer Science}, month = {October}, year = {2006}, address = {Berkeley, CA}, pages = {411-419}, eprint = {arXiv:quant-ph/0604141}, notes = {Upper bound on the depolarizing threshold of 45\%.} } @ARTICLE{Calderbank96, author = {A. R. Calderbank and Peter W. Shor}, title = {Good Quantum Error-Correcting Codes Exist}, journal = {Phys. Rev. A}, volume = {54}, pages = {1098}, year = {1996}, eprint = {arXiv:quant-ph/9512032} } @article{Calderbank97, Author = {A. R. Calderbank and E. M. Rains and P. W. Shor and N. J. A. Sloane}, Journal = {Phys. Rev. Lett.}, Month = {Jan}, Number = {3}, Numpages = {3}, Pages = {405--408}, Publisher = {American Physical Society}, Title = {Quantum Error Correction and Orthogonal Geometry}, Volume = {78}, Year = {1997} notes = {Perhaps the second appearance of the stabilizer formalism. Includes the paired-stabilizer form. } } @article{Chen08, author = {Xie Chen and Hyeyoun Chung and Andrew W. Cross and Bei Zeng and Isaac L. Chuang}, collaboration = {}, title = {Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit}, publisher = {APS}, year = {2008}, journal = {Phys. Rev. A}, volume = {78}, number = {1}, eid = {012353}, pages = {012353}, keywords = {binary codes; encoding; Hilbert spaces; quantum computing; quantum gates; teleportation}, doi = {10.1103/PhysRevA.78.012353}, eprint = {arXiv:0801.2360} } @article{Dawson06, author = {Christopher M. Dawson and Michael A. Nielsen}, title = {The Solovay-Kitaev algorithm}, journal = {Quant. Inf. Comp.}, volume = {6}, number = {1}, pages = {81--95}, year = {2006}, eprint = {arXiv:quant-ph/0505030} } @Article{DiVincenzo96, title = {Fault-Tolerant Error Correction with Efficient Quantum Codes}, author = {David P. DiVincenzo and Peter W. Shor}, journal = {Phys. Rev. Lett.}, volume = {77}, number = {15}, pages = {3260--3263}, numpages = {3}, year = {1996}, month = {Oct}, eprint = {arXiv:quant-ph/9605031}, notes = {The first paper to appear on fault tolerance.} } @Article{DiVincenzo98, title = {Quantum-channel capacity of very noisy channels}, author = {David P. DiVincenzo and Peter W. Shor and John A. Smolin}, journal = {Phys. Rev. A}, volume = {57}, number = {2}, pages = {830--839}, numpages = {9}, year = {1998}, month = {Feb}, publisher = {American Physical Society}, eprint = {arXiv:quant-ph/9706061} } @unpublished{EastinResidualError, author = {Bryan Eastin}, title = {Threshold estimates for non-depolarizing error models}, note = {In preparation} } @article{Eastin07, author = {Bryan Eastin}, title = {Fault-tolerant thresholds for encoded ancillae with homogeneous errors}, year = {2007}, journal = {Phys. Rev. A}, volume = {75}, number = {2}, eid = {022301}, numpages = {13}, pages = {022301}, eprint = {arXiv:quant-ph/0605192}, keywords = {quantum computing; fault tolerant computing; encoding; error analysis} } @article{Elliott07, author = {Matthew B. Elliott and Bryan Eastin and Carlton M. Caves}, title = {Graphical description of the action of {C}lifford operators on stabilizer states}, year = {2007}, eprint = {arXiv:quant-ph/0703278}, } @Article{Hamming50, title = {Error Detecting and Error Correcting Codes}, author = {Richard W. Hamming}, journal = {Bell Syst. Tech. J.}, volume = {29}, pages = {147-160}, year = {1950} } @misc{Gallager63, author = {Robert G. Gallager}, title = {Low-Density Parity-Check Codes}, year = {1963}, note = {Expanded version of 1960 M.I.T. Dissertation} } @article{Glancy06, author = {S. Glancy and E. Knill and H. M. Vasconcelos}, title = {Entanglement purification of any stabilizer state}, publisher = {APS}, year = {2006}, journal = {Phys. Rev. A}, volume = {74}, number = {3}, eid = {032319}, numpages = {11}, pages = {032319}, keywords = {quantum entanglement; error correction codes; error detection codes}, } @article{Gottesman96, Author = {Gottesman, Daniel}, Date-Added = {2007-03-31 10:50:53 -0600}, Date-Modified = {2007-03-31 10:50:54 -0600}, Doi = {10.1103/PhysRevA.54.1862}, Journal = {Phys. Rev. A}, Month = {Sep}, Number = {3}, Numpages = {6}, Pages = {1862--1868}, Publisher = {American Physical Society}, Title = {Class of quantum error-correcting codes saturating the quantum Hamming bound}, Volume = {54}, Year = {1996} notes = {I believe this is the first appearance of the stabilizer formalism.} } @phdthesis{Gottesman97, author = {Daniel Gottesman}, title = {Stabilizer Codes and Quantum Error Correction}, school = {California Institute of Technology}, year = {1997} eprint = {arXiv:quant-ph/9705052} } @Article{Gottesman98, title = {Theory of fault-tolerant quantum computation}, author = {Daniel Gottesman}, journal = {Phys. Rev. A}, volume = {57}, number = {1}, pages = {127--137}, numpages = {10}, year = {1998}, month = {Jan}, notes = {I have omitted the arxiv reference here because it doesn't include Gottesman's proof that H, P, and CX generate the Clifford group.} } @ARTICLE{Gottesman99, author = {Daniel Gottesman and Isaac L. Chuang}, title = {Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations}, journal = {Nature}, volume = {402}, pages = {390--393}, year = {1999}, eprint = {arXiv:quant-ph/9908010} } @Article{Gottesman01, title = {Secure quantum key distribution using squeezed states}, author = {Daniel Gottesman and John Preskill}, journal = {Phys. Rev. A}, volume = {63}, number = {2}, pages = {022309}, numpages = {18}, year = {2001}, month = {Jan}, publisher = {American Physical Society}, eprint = {arXiv:quant-ph/0008046}, } @ARTICLE{Grassl02, title={Graphs, quadratic forms, and quantum codes}, author={M. Grassl and A. Klappenecker and M. Rotteler}, journal={Proceedings of the IEEE International Symposium on Information Theory}, year={2002}, pages={45}, keywords={ error correction codes, graph theory, quantum communication additive group, error-correcting codes, finite field, graphical quantum code, quadratic forms, stabilizer code, undirected graph}, doi={10.1109/ISIT.2002.1023317} } @book{Hall, author = {Brian C. Hall}, title = {Lie Groups, Lie Algebras, and Representations: An Elementary Introduction}, year = {2004}, publisher = {Springer}, address = {New York, USA}, } @Article{Hamada04, title = {Reliability of {C}alderbank-{S}hor-{S}teane codes and security of quantum key distribution}, author = {Mitsuru Hamada}, journal = {J. Phys. A}, volume = {37}, number={34}, pages = {8303--8328}, year = {2004}, eprint = {arXiv:quant-ph/0308029}, } @inproceedings{Kitaev97, author = {Alexi Kitaev}, title = {Quantum error correction with imperfect gates}, booktitle = {Proceeding of the Third International Conference on Quantum Communication and Measurement}, year = {1997}, \notes{ed. O. Hirota, A. S. Holevo, and C. M. Caves (New York, Plenum, 1997).} eprint = {arXiv:quant-ph/9611025}, } @article{Kitaev97b, author = {Alexi Yu Kitaev}, title = {Quantum computations: algorithms and error correction}, journal = {Russ. Math. Surv.}, volume = {52}, number = {6}, pages = {1191--1249}, year = {1997}, notes = {First published appearance of the Solovay-Kitaev algorithm.} } @ARTICLE{Knill98, author = {Emanuel Knill and Raymond Laflamme and Wojciech Zurek}, title = {Resilient quantum computation: Error models and thresholds}, journal = {Proc. R. Soc. London, Ser. A}, volume = {454}, pages = {365--384}, year = {1998}, eprint = {arXiv:quant-ph/9702058} } @MISC{Knill04, title = {Fault-tolerant postselected quantum computation: Schemes}, author = {Emanuel Knill}, year = {2004}, eprint = {arXiv:quant-ph/0402171} } @ARTICLE{Knill05, author = {Emanuel Knill}, title = {Quantum Computing with Realistically Noisy Devices}, journal = {Nature}, volume = {434}, pages = {39--44}, year = {2005}, eprint = {arXiv:quant-ph/0410199}, notes = {Estimates the depolarizing threshold at 3\% to 5\%.} } @article{Knill05b, author = {Emanuel Knill}, title = {Scalable quantum computing in the presence of large detected-error rates}, publisher = {APS}, year = {2005}, journal = {Phys. Rev. A}, volume = {71}, number = {4}, eid = {042322}, numpages = {7}, pages = {042322}, keywords = {quantum computing; teleportation; error detection; error correction; information theory; Bell theorem}, eprint = {arXiv:quant-ph/0312190}, notes = {Is this wrong??? Estimates the depolarizing threshold at 3\% to 5\%.} } @book{MacKay, author = {David J. C. MacKay}, title = {Information Theory, Inference and Learning Algorithms}, year = {2003}, publisher = {Cambridge University Press}, address = {New York, NY, USA}, } @inproceedings{MacKay95, author = {David J.C. MacKay and Radford M. Neal}, title = {Good Codes based on Very Sparse Matrices}, booktitle = {IMA: IMA Conference on Cryptography and Coding}, notes{held in Santa Fe, New Mexico}, year={1995} } @book{MacWilliamsSloane, author = {F.J. MacWilliams and N.J.A. Sloane}, title = {The Theory of Error-Correcting Codes}, year = {1977}, publisher = {North-Holland}, address = {Amsterdam, The Netherlands} } @article{Mermin90, author = {N. David Mermin}, title = {What's Wrong with These Elements of Reality?}, journal = {Physics Today}, pages = {9-11}, month = {June}, year = {1990} } @article{Mochon04, author = {Carlos Mochon}, title = {Anyon computers with smaller groups}, year = {2004}, journal = {Phys. Rev. A}, volume = {69}, number = {3}, eid = {032306}, numpages = {26}, pages = {032306}, keywords = {anyons; gauge field theory; group theory; quantum gates; probability}, eprint = {arXiv:quant-ph/0306063} notes = {Has a section on dealing with leakage.} } @MISC{Mosca08, title = {Quantum Algorithms}, author = {Michele Mosca}, year = {2008}, eprint = {arXiv:0808.0369} } @book{Munkres, author = {James R. Munkres}, title = {Topology}, edition = {Second}, year = {2000}, publisher = {Prentice Hall}, address = {New Jersey, USA}, } @book{NielsenChuang, author = {Michael A. Nielsen and Isaac L. Chuang}, title = {Quantum computation and quantum information}, year = {2000}, publisher = {Cambridge University Press}, address = {Cambridge, England} } @article{Pan00, author = {Jian-Wei Pan and Dik Bouwmeester and Matthew Daniell and Harald Weinfurter and Anton Zeilinger}, title = {Experimental test of quantum nonlocality in three-photon {G}reenberger-{H}orne-{Z}eilinger entanglement}, journal = {Nature}, month = {February}, volume = {403}, year = {2000}, pages = {515-519}, notes = {Experimental violation of a CHSH Bell inequality.} } @incollection{Preskill98, author = {John Preskill}, title = {Fault-tolerant Quantum Computation}, booktitle = {Introduction to Quantum Computation}, publisher = {World Scientific}, year = {1998}, eprint = {arXiv:quant-ph/9712048} } @MISC{Preskill00, title = {Quantum clock synchronization and quantum error correction}, author = {John Preskill}, year = {2000}, eprint = {arXiv:quant-ph/0010098v1} } @MISC{PreskillNotes, author = {John Preskill}, title = {Lecture Notes for Physics 229: Quantum Information and Computation}, url = {http://www.iqi.caltech.edu}{http://www.iqi.caltech.edu}, } @Article{Raussendorf01, title = {A One-Way Quantum Computer}, author = {Robert Raussendorf and Hans J.Briegel}, journal = {Phys. Rev. Lett.}, volume = {86}, number = {22}, pages = {5188--5191}, numpages = {3}, year = {2001}, month = {May}, notes = {The debut of the one-way quantum computer.} } @article{Razborov03, author = {Alexander A. Razborov}, title = {An Upper Bound on the Threshold Quantum Decoherence Rate}, journal = {Quantum Information and Computation}, volume = {4}, number = {3}, pages = {222-228}, year = {2003}, eprint = {arXiv:quant-ph/0310136}, notes = {Upper bound on the depolarizing threshold of 50\%.} } @Article{Reck94, title = {Experimental realization of any discrete unitary operator}, author = {Michael Reck and Anton Zeilinger and Herbert J. Bernstein and Philip Bertani}, journal = {Phys. Rev. Lett.}, volume = {73}, number = {1}, pages = {58--61}, numpages = {3}, year = {1994}, month = {Jul}, notes = {Shows that an arbitrary unitary can be decomposed into two-level transitions.} } @MISC{Reichardt04, author = {Ben W. Reichardt}, title = {Improved ancilla preparation scheme increases fault-tolerant threshold}, year = {2004}, eprint = {arXiv:quant-ph/0406025} } @incollection{Reichardt05, author = {Ben W. Reichardt}, title = {Fault-tolerance threshold for a distance-three quantum code}, booktitle = {Automata, Languages and Programming}, publisher = {Springer Berlin}, address = {Heidelberg}, volume = {4051}, pages = {50-61}, year = {2006}, eprint = {arXiv:quant-ph/0509203} } @inproceedings{Reichardt06, author = {Ben W. Reichardt}, title = {Postselection threshold against biased noise}, booktitle = {Foundations of Computer Science, 2006. FOCS '05. 47th Annual IEEE Symposium}, pages = {420-428}, year={2006} } @article{Rowe01, author = {M. A. Rowe and D. Kielpinski and V. Meyer and C. A. Sackett and W. M. Itano and C. Monroe and D. J. Wineland}, title = {Experimental violation of a Bell's inequality with efficient detection}, journal = {Nature}, month = {February}, volume = {409}, year = {2001}, pages = {791-794}, notes = {Experimental violation of a CHSH Bell inequality claimed to close both detection and locality loopholes.} } @article{Schlingemann02, title = {Quantum error-correcting codes associated with graphs}, author = {Dirk Schlingemann and Reinhard F. Werner}, journal = {Phys. Rev. A}, volume = {65}, number = {1}, pages = {012308}, year = {2002}, month = {Dec}, doi = {10.1103/PhysRevA.65.012308}, publisher = {American Physical Society} eprint = {arXiv:quant-ph/0012111} } @article{Schlingemann02b, author = {Dirk Schlingemann}, title = {Stabilizer codes can be realized as graph codes}, year = {2002}, journal = {Quant. Inf. Comp.}, volume = {2}, number = {4}, pages = {307-323}, eprint = {arXiv:quant-ph/0111080} } @article{Schlingemann04, author = {Dirk Schlingemann}, title = {Cluster states, algorithms and graphs}, year = {2004}, journal = {Quant. Inf. Comp.}, volume = {4}, number = {4}, pages = {287-324}, eprint = {arXiv:quant-ph/0305170} } @book{Sepanski, author = {Mark R. Sepanski}, title = {Compact Lie Groups}, year = {2007}, publisher = {Springer}, address = {New York, USA} } @Article{Shannon48, title = {A Mathematical theory of communication}, author = {Claude E. Shannon}, journal = {Bell Syst. Tech. J.}, volume = {27}, pages = {379}, year = {1948} } @inproceedings{Shor94, author = {Peter W. Shor}, title = {Algorithms for quantum computation: Discrete logarithms and factoring}, booktitle = {Proc. 35th Symp. Found. Comp. Sci.}, pages = {124}, year = {1994}, eprint = {arXiv:quant-ph/9508027}, notes = {Held in Santa Fe, New Mexico. This was the debut of the quantum fourier transform.} } @ARTICLE{Shor95, author = {Peter W. Shor}, title = {Scheme for reducing decoherence in quantum memory}, journal = {Phys. Rev. A 52}, volume = {52}, pages = {2493--2496}, year = {1995} } @inproceedings{Shor97, author = {P.W. Shor}, title = {Fault-tolerant quantum computation}, booktitle = {Proc. 37th Symp. Found. Comp. Sci.}, pages = {56}, year = {1996}, eprint = {arXiv:quant-ph/9605011}, notes = {The second appearance of fault tolerance occurred at the 1996 Foundations of Computer Science conference in Burlington, Vermont. The paper appeared in the conference proceedings.} } @Article{Steane96, title = {Error Correcting Codes in Quantum Theory}, author = {Andrew M. Steane}, journal = {Phys. Rev. Lett.}, volume = {77}, number = {5}, pages = {793--797}, numpages = {4}, year = {1996}, month = {Jul}, } @ARTICLE{Steane96b, author = {Andrew M. Steane}, title = {Multiple Particle Interference and Quantum Error Correction}, journal = {Proc. R. Soc. A}, volume = {452}, pages = {2551}, year = {1996}, eprint = {arXiv:quant-ph/9601029} } @Article{Steane97, title = {Active Stabilization, Quantum Computation, and Quantum State Synthesis}, author = {Andrew M. Steane}, journal = {Phys. Rev. Lett.}, volume = {78}, number = {11}, pages = {2252--2255}, numpages = {3}, year = {1997}, month = {Mar}, eprint = {arXiv:quant-ph/9611027} } @ARTICLE{Steane98, author = {Andrew M. Steane}, title = {Space, time, parallelism and noise requirements for reliable quantum computing}, journal = {Fortsch. Phys.}, volume = {46}, pages = {443}, year = {1998}, eprint = {arXiv:quant-ph/9708021}, } @article{Steane03, author = {Andrew M. Steane}, collaboration = {}, title = {Overhead and noise threshold of fault-tolerant quantum error correction}, publisher = {APS}, year = {2003}, journal = {Phys. Rev. A}, volume = {68}, number = {4}, eid = {042322}, numpages = {19}, pages = {042322}, keywords = {quantum theory; error correction; quantum computing}, eprint = {arXiv:quant-ph/0207119}, } @article{Svore05, author = {Krysta M. Svore and Barbara M. Terhal and David P. DiVincenzo}, collaboration = {}, title = {Local fault-tolerant quantum computation}, publisher = {APS}, year = {2005}, journal = {Phys. Rev. A}, volume = {72}, number = {2}, eid = {022317}, numpages = {17}, pages = {022317}, keywords = {quantum computing; fault tolerant computing; concatenated codes; quantum noise; error correction}, eprint = {arXiv:quant-ph/0410047}, } @article{Svore06, author = {Krysta M. Svore and A. W. Cross and Isaac L. Chuang and A. V. Aho}, title = {A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing}, journal = {Quantum Information and Computation}, volume = {6}, number = {3}, pages = {193-212}, year = {2006}, eprint = {arXiv:quant-ph/0508176} } @article{Tessier05, author = {Tracey E. Tessier and Carlton M. Caves and Ivan H. Deutsch and Bryan Eastin and Dave Bacon}, title = {Optimal classical-communication-assisted local model of n-qubit {G}reenberger-{H}orne-{Z}eilinger correlations}, year = {2005}, journal = {Phys. Rev. A}, volume = {72}, number = {3}, eid = {032305}, numpages = {5}, pages = {032305}, eprint = {arXiv:quant-ph/0603032}, keywords = {quantum computing; quantum entanglement} } @article{VandenNest04, author = {Maarten Van den Nest and Jeroen Dehaene and Bart De Moor}, title = {Graphical description of the action of local {C}lifford transformations on graph states}, publisher = {APS}, year = {2004}, journal = {Phys. Rev. A}, volume = {69}, number = {2}, eid = {022316}, pages = {022316}, keywords = {graph theory; information theory; group theory; quantum computing}, eprint = {arXiv:quant-ph/0308151} } @article{VandenNest05, author = {Maarten Van den Nest and Jeroen Dehaene and Bart De Moor}, title = {Local unitary versus local Clifford equivalence of stabilizer states}, publisher = {APS}, year = {2005}, journal = {Phys. Rev. A}, volume = {71}, number = {6}, eid = {062323}, pages = {062323}, keywords = {quantum computing; stochastic processes; polynomials}, doi = {10.1103/PhysRevA.71.062323} } @article{VandenNest05, author = {Maarten Van den Nest and Jeroen Dehaene and Bart De Moor}, title = {Local unitary versus local Clifford equivalence of stabilizer states}, publisher = {APS}, year = {2005}, journal = {Phys. Rev. A}, volume = {71}, number = {6}, eid = {062323}, pages = {062323}, keywords = {quantum computing; stochastic processes; polynomials}, doi = {10.1103/PhysRevA.71.062323} } @MISC{Wikipedia, url = {http://www.wikipedia.org/} } @MISC{Zalka96, author = {Christof Zalka}, title = {Threshold estimate for fault tolerant quantum computation}, eprint = {arXiv:quant-ph/9612028}, year = {1997}, } @MISC{Zeng07, author = {Bei Zeng and Andrew Cross and Isaac L. Chuang}, title = {Transversality versus Universality for Additive Quantum Codes}, year = {2007}, eprint = {arXiv:0706.1382} } @Article{Zhou00, author = {Xinlan Zhou and Debbie W. Leung and Isaac L. Chuang}, title = {Methodology for quantum logic gate construction}, journal = {Phys. Rev. A}, volume = {62}, number = {5}, pages = {052316}, numpages = {12}, year = {2000}, month = {Oct}, eprint = {arXiv:quant-ph/0002039}, doi = {10.1103/PhysRevA.62.052316}, publisher = {American Physical Society} }