[ADH+09] A., Abeyesinghe, I., Devetak, P., Hayden, and A., Winter. 2009. The mother of all protocols: Restructuring quantum information's family tree. Proc. R. Soc. London Ser. A, 465, 2537.Google Scholar

[A61] A., Abragam. 1961. The Principles of Nuclear Magnetism. International Series of Monographs on Physics. London: Oxford University Press.Google Scholar

[AL91] I., Affleck and A. W. W., Ludwig. 1991. Critical theory of overscreened Kondo fixed points. Nucl. Phys. B, 360, 641.Google Scholar

[A00a] G., Agarwal. 2000. Control of decoherence and relaxation by frequency modulation of a heat bath. Phys. Rev. A, 61, 013809.Google Scholar

[A10] G. S., Agarwal. 2010. Saving entanglement via a nonuniform sequence of π pulses. Phys. Scr., 82, 038103.Google Scholar

[AC08] V., Aggarwal and A. R., Calderbank. 2008. Boolean functions, projection operators and quantum error correcting codes. IEEE Trans. Inf. Theory, 54, 1700.Google Scholar

[A00b] D., Aharonov. 2000. Quantum to classical phase transition in noisy quantum computers. Phys. Rev. A, 6206, 062311.Google Scholar

[AB.-O08] D., Aharonov and M., Ben-Or. 2008. Fault-tolerant quantum computation with constant error rate. SIAM J. Comput., 38, 1207.Google Scholar

[AB.-OI+96] D., Aharonov, M., Ben-Or, R., Impagliazzo, and N., Nisan. 1996. Limitations of noisy reversible computation. eprint arXiv:quant-ph/9611028.Google Scholar

[AKP06] D., Aharonov, A., Kitaev, and J., Preskill. 2006. Fault-tolerant quantum computation with long-range correlated noise. Phys. Rev. Lett., 96, 050504.Google Scholar

[AV89] Y., Aharonov and L., Vaidman. 1989. Aharonov and Vaidman reply. Phys. Rev. Lett., 62, 2327.Google Scholar

[AV90] Y., Aharonov and L., Vaidman. 1990. Properties of a quantum system during the time interval between two measurements. Phys.Rev. A, 41, 11.Google Scholar

[AAV88] Y., Aharonov, D. Z., Albert, and L., Vaidman. 1988. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett., 60, 1351.Google Scholar

[ADL02] C., Ahn, A. C., Doherty, and A. J., Landahl. 2002. Continuous quantum error correction via quantum feedback control. Phys.Rev. A, 65, 042301.Google Scholar

[AWM03] C., Ahn, H. W., Wiseman, and G. J., Milburn. 2003. Quantum error correction for continuously detected errors. Phys.Rev. A, 67, 052310.Google Scholar

[AM00] S., Aji and R., McEliece. 2000. The generalized distributive law. IEEE Trans. Inf. Theory, 46, 325.Google Scholar

[AAS11] A., Ajoy, G. A., Álvarez, and D., Suter. 2011. Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath. Phys.Rev. A, 83, 032303.Google Scholar

[A.-HDD+06] K. A., Al-Hassanieh, V. V., Dobrovitski, E., Dagotto, and B. N., Harmon. 2006. Numerical modeling of the central spin problem using the spin-coherent-state P representation. Phys. Rev. Lett., 97, 037204.Google Scholar

[A88] R., Alicki. 1988. Limited thermalization for the Markov mean-field model of N atoms in thermal field. Physica A, 150, 455.Google Scholar

[A06] R., Alicki. 2006. Quantum error correction fails for Hamiltonian models. Fluct. Noise Lett., 6, C23.Google Scholar

[A09] R., Alicki. 2009. Quantum memory as a perpetuum mobile of the second kind. eprint arXiv:0901.0811.Google Scholar

[AF01] R., Alicki and M., Fannes. 2001. Quantum Dynamical Systems. Oxford: Oxford University Press.Google Scholar

[AF09] R., Alicki and M., Fannes. 2009. Decay of fidelity in terms of correlation functions. Phys. Rev. A, 79, 012316.Google Scholar

[AL07] R., Alicki and K., Lendi. 2007. Quantum Dynamical Semigroups and Applications 2nd edn., Lecture Notes in Physics, Volume 717. Berlin: Springer.Google Scholar

[AHH+02] R., Alicki, M., Horodecki, P., Horodecki, and R., Horodecki. 2002. Dynamical description of quantum computing: Generic nonlocality of quantum noise. Phys. Rev. A, 65, 062101.Google Scholar

[AHH+04] R., Alicki, M. L., Horodecki, P. L., Horodecki, and R., Horodecki. 2004. Thermodynamics of quantum information systems. Hamiltonian description. Open Syst. Inf. Dyn., 11, 205.Google Scholar

[ALZ06] R., Alicki, D. A., Lidar, and P., Zanardi. 2006. Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit. Phys. Rev. A, 73, 052311.Google Scholar

[AFH07] R., Alicki, M., Fannes, and M., Horodecki. 2007. A statistical mechanics view on Kitaev's proposal for quantum memories. J. Phys. A, 40, 6451.Google Scholar

[AFH09] R., Alicki, M., Fannes, and M., Horodecki. 2009. On thermalization in Kitaev's 2D model. J. Phys. A, 42, 065303.Google Scholar

[AHH+10] R., Alicki, M., Horodecki, P., Horodecki, and R., Horodecki. 2010. On thermal stability of topological qubit in Kitaev's 4D model. Open Syst. Inf. Dyn., 17, 1.Google Scholar

[A07] P., Aliferis. 2007. Level Reduction and the Quantum Threshold Theorem. Ph.D. thesis, California Institute of Technology. eprint arXiv:quant-ph/0703230.Google Scholar

[AC07] P., Aliferis and A. W., Cross. 2007. Subsystem fault tolerance with the Bacon—Shor code. Phys. Rev. Lett., 98, 220502.Google Scholar

[AL04] P., Aliferis and D. W., Leung. 2004. Computation by measurements: A unifying picture. Phys. Rev. A, 70, 062314.Google Scholar

[AL06] P., Aliferis and D. W., Leung. 2006. Simple proof of fault tolerance in the graph-state model. Phys.Rev.A, 73, 032308.Google Scholar

[AP08] P., Aliferis and J., Preskill. 2008. Fault-tolerant quantum computation against biased noise. Phys. Rev. A, 78, 052331.Google Scholar

[AP09] P., Aliferis and J., Preskill. 2009. The Fibonacci scheme for fault-tolerant quantum computation. Phys. Rev. A, 79, 012332.Google Scholar

[AT07] P., Aliferis and B. M., Terhal. 2007. Fault-tolerant quantum computation for local leakage faults. Quant. Inf. Comput., 7, 139.Google Scholar

[AGP06] P., Aliferis, D., Gottesman, and J., Preskill. 2006. Quantum accuracy threshold for concatenated distance-3 codes. Quant. Inf. Comput., 6, 97.Google Scholar

[AGP08] P., Aliferis, D., Gottesman, and J., Preskill. 2008. Accuracy threshold for postselected quantum computation. Quant. Inf. Comput., 8, 181.Google Scholar

[AS11] G. A., Alvarez and D., Suter. 2011. Dynamical decoupling noise spectroscopy. eprint arXiv:1106.3463.Google Scholar

[AAP+10] G. A., Álvarez, A., Ajoy, X., Peng, and D., Suter. 2010. Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath. Phys. Rev. A, 82, 042306.Google Scholar

[A08] S., Aly. 2008. A class of quantum LDPC codes constructed from finite geometries. IEEE Global Telecommunications Conference, p.1.Google Scholar

[A54] P. W., Anderson. 1954. A mathematical model for the narrowing of spectral lines by exchange or motion. J. Phys. Soc. Jpn., 9, 316.Google Scholar

[ADD+07] K. S., Andrews, D., Divsalar, S., Dolinar, J., Hamkins, C. R., Jones, and F., Pollara. 2007. The development of turbo and LDPC codes for deep space applications. Proc. IEEE, Special Issue on “Technical Advances in Deep Space Communications and Tracking”, 95, 2142.Google Scholar

[ATK+09] T., Aoki, G., Takahashi, T., Kajiya, J., Yoshikawa, S. L., Braunstein, P., van Loock, and A., Furusawa. 2009. Quantum error correction beyond qubits. Nature Phys., 5, 541.Google Scholar

[AL70] H., Araki and E. H., Lieb. 1970. Entropy inequalities. Commun. Math. Phys., 18, 160.Google Scholar

[AK01] A., Ashikhmin and E., Knill. 2001. Nonbinary quantum stabilizer codes. IEEE Trans. Inf. Theory, 47, 3065.Google Scholar

[AD02] K., Audenaert and B., De Moor. 2002. Optimizing completely positive maps using semidefinite programming. Phys. Rev. A, 65, 030302(R).Google Scholar

[B06] D., Bacon. 2006. Operator quantum error-correcting subsystems for self-correcting quantum memories. Phys. Rev. A, 73, 12340.Google Scholar

[BC06] D., Bacon and A., Casaccino. 2006. Quantum error correcting subsystem codes from two classical linear codes. 44th Annual Alerton Conferences. eprint arXiv:quant-ph/0610088.Google Scholar

[BL+99] D., Bacon, D. A., Lidar, and K., Whaley. 1999. Robustness of decoherence-free subspaces for quantum computation. Phys. Rev. A, 60, 1944.Google Scholar

[BKL+00] D., Bacon, J., Kempe, D. A., Lidar, and K. B., Whaley. 2000. Universal fault-tolerant computation on decoherence-free subspaces. Phys. Rev. Lett., 85, 1758.Google Scholar

[BBW01] D., Bacon, K., Brown, and K., Whaley. 2001. Coherence-preserving quantum bits. Phys. Rev. Lett., 87, 247902.Google Scholar

[BLW83] R. D., Baker, vJ. H., Lint, and R. M., Wilson. 1983. On the Preparata and Goethals codes. IEEE Trans. Inf. Theory, 29, 342.Google Scholar

[BW06] K., Banaszek and W., Wasilewski. 2006. Linear-optics manipulations of photon-loss codes. Proceedings of NATO Advanced Research Workshop “Quantum Communication and Security”. Institute of Theoretical Physics and Astrophysics, Gdansk, Poland.Google Scholar

[B82] F., Barahona. 1982. On the computational complexity of Ising spin glass models. J. Phys. A, 15, 3241.Google Scholar

[BBD+97] A., Barenco, A., Berthiaume, D., Deutsch, A., Eckert, R., Jozsa, and C., Macchiavello. 1997. Stabilization of quantum computations by symmetrization. SIAM J. Comput., 26, 1541.Google Scholar

[B04] R., Barnes. 2004. Stabilizer codes for continuous-variable quantum error correction. arXiv:quant-ph/0405064.Google Scholar

[BK02] H., Barnum and E., Knill. 2002. Reversing quantum dynamics with near-optimal quantum and classical fidelity. J. Math. Phys., 43, 2097.Google Scholar

[BKN00] H., Barnum, E., Knill, and M. A., Nielsen. 2000. On quantum fidelities and channel capacities. IEEE Trans. Inf. Theory, 46, 1317.Google Scholar

[BMM+10] C., Barthel, J., Medford, C. M., Marcus, M. P., Hanson, and A. C., Gossard. 2010. Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit. Phys. Rev. Lett., 105, 266808.Google Scholar

[BMR+06] J., Baugh, O., Moussa, C. A., Ryan, R., Laflamme, C., Ramanathan, T. F., Havel, and D. G., Cory. 2006. A solid-state NMR three-qubit homonuclear system for quantum information processing: Control and characterization. Phys. Rev. A, 73, 022305.Google Scholar

[B.-O02] M., Ben-Or. 2002. Security of BB84 QKD Protocol. MSRI: www.msri.org/publications/ln/msri/2002/quantumintro/ben-or/2/.Google Scholar

[B.-OHL+05] M. Ben-Or, M., Horodecki, D. W., Leung, D., Mayers, and J., Oppenheim. 2005. The universal composable security of quantum key distribution. Theory of Cryptography: Second Theory of Cryptography Conference. Lecture Notes in Computer Science, Vol. 3378, p. 387. Berlin: Springer Verlag.Google Scholar

[BH01] S. C., Benjamin and P. M., Hayden. 2001. Multiplayer quantum games. Phys. Rev. A, 64, 030301.Google Scholar

[B92] C. H., Bennett. 1992. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett., 68, 3121.Google Scholar

[BB84] C. H., Bennett and G., Brassard. 1984. Quantum cryptography: Public key distribution and coin tossing. Proceedings of IEEE International Conference on Computers Systems and Signal Processing, p. 175.Google Scholar

[BBM92] C. H., Bennett, G., Brassard, and N. D., Mermin. 1992. Quantum cryptography without Bell's theorem. Phys. Rev. Lett., 68, 557.Google Scholar

[BBC+93] C. H., Bennett, G., Brassard, C., Crépeau, R., Jozsa, A., Peres, and W. K., Wootters. 1993. Teleporting an unknown quantum state via dual classical and Einstein—Podolsky—Rosen channels. Phys. Rev. Lett., 70, 1895.Google Scholar

[BBP+96a] C. H., Bennett, H. J., Bernstein, S., Popescu, and B., Schumacher. 1996. Concentrating partial entanglement by local operations. Phys. Rev. A, 53, 2046.Google Scholar

[BDS+96] C. H., Bennett, D. P., DiVincenzo, J. A., Smolin, and W. K., Wootters. 1996. Mixed state entanglement and quantum error correction. Phys. Rev. A, 54, 3824.Google Scholar

[BBP+96b] C. H., Bennett, G., Brassard, S., Popescu, B., Schumacher, J. A., Smolin, and W. K., Wootters. 1996. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett., 76, 722.Google Scholar

[BCL+02] C. H., Bennett, J. I., Cirac, M. S., Leifer, D. W., Leung, N., Linden, S., Popescu, and G., Vidal. 2002. Optimal simulation of two-qubit Hamiltonians using general local operations. Phys.Rev.A, 66, 012305.Google Scholar

[BKK07a] C., Beny, A., Kempf, and D. W., Kribs. 2007. Generalization of quantum error correction via the Heisenberg picture. Phys. Rev. Lett., 98, 100502.Google Scholar

[BKK07b] C., Beny, A., Kempf, and D. W., Kribs. 2007. Quantum error correction of observables. Phys. Rev. A, 76, 042303.Google Scholar

[BKK09] C., Beny, A., Kempf, and D. W., Kribs. 2009. Quantum error correction on infinite-dimensional Hilbert spaces. J. Math. Phys., 50, 062108.Google Scholar

[B01] A. J., Berglund. 2001. Quantum coherence and control in one- and two-photon optical systems. eprint arXiv:quant-ph/0010001.Google Scholar

[BMT78] E. R., Berlekamp, R. J., McEliece, and H. C., A. Van Tilborg. 1978. On the inherent intractability of certain coding problems. IEEE Trans. Inf. Theory, 24, 384.Google Scholar

[BV97] E., Bernstein and U., Vazirani. 1997. Quantum complexity theory. SIAM J. Comput., 26, 11.Google Scholar

[BGT93] C., Berrou, A., Glavieux, and P., Thitimajshima. 1993. Near Shannon limit error-correcting coding and decoding. ICC'93, p. 1064.Google Scholar

[B84] M., Berry. 1984. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. London Ser. A, 392, 45.Google Scholar

[BJL99] T., Beth, D., Jungnickel, and H., Lenz. 1999. Design Theory. Encyclopedia of Mathematics and Its Applications, Vol. I. Cambridge: Cambridge University Press.Google Scholar

[B97] R., Bhatia. 1997. Matrix Analysis. Graduate Texts in Mathematics. New York: Springer-Verlag.Google Scholar

[BUV+09a] M. J., Biercuk, H., Uys, A. P., VanDevender, N., Shiga, W. M., Itano, and J. J., Bollinger. 2009. Optimized dynamical decoupling in a model quantum memory. Nature, 458, 996.Google Scholar

[BUV+09b] M. J., Biercuk, H., Uys, A. P., VanDevender, N., Shiga, W. M., Itano, and J. J., Bollinger. 2009. Experimental Uhrig dynamical decoupling using trapped ions. Phys. Rev. A, 79, 062324.Google Scholar

[BDU11] M. J., Biercuk, A. C., Doherty, and H., Uys. 2011. Dynamical decoupling as a filter design problem. J. Phys. B, 44, 154002.Google Scholar

[BIZ+00] E., Biolatti, R., Iotti, P., Zanardi, and F., Rossi. 2000. Quantum information processing with semiconductor macroatoms. Phys. Rev. Lett., 85, 5647.Google Scholar

[BHW+04] A., Blais, R.-S., Huang, A., Wallraff, S. M., Girvin, and R. J., Schoelkopf. 2004. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A, 69, 062320.Google Scholar

[BCO+09] S., Blanes, F., Casas, J., Oteo, and J., Ros. 2009. The Magnus expansion and some of its applications. Phys. Rep., 470, 151.Google Scholar

[BFN+11] H., Bluhm, S., Foletti, I., Neder, M., Rudner, D., Mahalu, V., Umansky, and A., Yacoby. 2011. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs. Nature Phys., 7, 109.Google Scholar

[B.-KNP+08] R., Blume-Kohout, H. K., Ng, D., Poulin, and L., Viola. 2008. Characterizing the structure of preserved information in quantum processes. Phys. Rev. Lett., 100, 030501.Google Scholar

[B98a] B., Bollobás. 1998. Modern Graph Theory. New York: Springer-Verlag.Google Scholar

[B10a] H., Bombin. 2010. Topological order with a twist: Ising anyons from an Abelian model. Phys. Rev. Lett., 105, 030403.Google Scholar

[B10b] H., Bombin. 2010. Topological subsystem codes. Phys. Rev. A, 81, 032301.Google Scholar

[B11a] H., Bombin. 2011. Clifford gates by code deformation. New J. Phys., 13, 043005.Google Scholar

[B11b] H., Bombin. 2011. Structure of 2D topological stabilizer codes. eprint arXiv:1107.2707.Google Scholar

[BM.-D06] H., Bombin and M., Martin-Delgado. 2006. Topological quantum distillation. Phys. Rev. Lett., 97, 180501.Google Scholar

[BM.-D07a] H., Bombin and M., Martin-Delgado. 2007. Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates. Phys. Rev. B, 75, 75103.Google Scholar

[BM.-D07b] H., Bombin and M., Martin-Delgado. 2007. Topological computation without braiding. Phys. Rev. Lett., 98, 160502.Google Scholar

[BM.-D09] H., Bombin and M., Martin-Delgado. 2009. Quantum measurements and gates by code deformation. J. Phys. A, 42, 095302.Google Scholar

[BCH+09] H., Bombin, R., Chhajlany, M., Horodecki, and M., Martin-Delgado. 2009. Self-correcting quantum computers. eprint arXiv:0907.5228.Google Scholar

[BD.-CP11] H., Bombin, G., Duclos-Cianci, and D., Poulin. 2011. Universal topological phase of 2D stabilizer codes. eprint arXiv:1103.4606.Google Scholar

[BCP97] W., Bosma, J. J., Cannon, and C., Playoust. 1997. The MAGMA algebra system I: The user language. J. Symb. Comput., 24, 235.Google Scholar

[BPF+02] N., Boulant, M. A., Pravia, E. M., Fortunato, T. F., Havel, and D. G., Cory. 2002. Experimental concatenation of quantum error correction with decoupling. Quant. Inf. Proc., 1, 135.Google Scholar

[BVF+05] N., Boulant, L., Viola, E. M., Fortunato, and D. G., Cory. 2005. Experimental implementation of a concatenated quantum error-correcting code. Phys. Rev. Lett., 94, 130501.Google Scholar

[B02a] G., Bowen. 2002. Entanglement required in achieving entanglement-assisted channel capacities. Phys. Rev. A, 66, 052313.Google Scholar

[BV04a] S., Boyd and L., Vandenberghe. 2004. Convex Optimization. Cambridge: Cambridge University Press.Google Scholar

[BMP+99] P. O., Boykin, T., Mor, M., Pulver, V., Roychowdhury, and F., Vatan. 1999. On universal and fault-tolerant quantum computing. Proceedings 40th FOCS. Society Press, p. 486.Google Scholar

[BV04b] F. G., S. L. Brandao and R. O., Vianna. 2004. Separable multipartite mixed states: Operational asymptotically necessary and sufficient conditions. Phys. Rev. Lett., 93, 220503.Google Scholar

[B98b] S. L., Braunstein. 1998. Error correction for continuous quantum variables. Phys. Rev. Lett., 80, 4084.Google Scholar

[B98c] S. L., Braunstein. 1998. Quantum error correction for communication with linear optics. Nature, 394, 47.Google Scholar

[B05] S. L., Braunstein. 2005. Squeezing as an irreducible resource. Phys.Rev.A, 71, 055801.Google Scholar

[BCJ+99] S. L., Braunstein, C. M., Caves, R., Jozsa, N., Linden, S., Popescu, and R., Schack. 1999. Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett., 83, 1054.Google Scholar

[B11c] S., Bravyi. 2011. Subsystem codes with spatially local generators. Phys. Rev. A, 83, 012320.Google Scholar

[BH11] S., Bravyi and J., Haah. 2011. On the energy landscape of 3D spin Hamiltonians with topological order. eprint arXiv:1105.4159.Google Scholar

[BK98] S., Bravyi and A., Kitaev. 1998. Quantum codes on a lattice with boundary. eprint arXiv:quant-ph/9811052.Google Scholar

[BK05] S., Bravyi and A., Kitaev. 2005. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A, 71, 022316.Google Scholar

[BT09] S., Bravyi and B., Terhal. 2009. A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes. New J. Phys., 11, 043029.Google Scholar

[BFG06] S., Bravyi, D., Fattal, and D., Gottesman. 2006. GHZ extraction yield for multipartite stabilizer states. J. Math. Phys., 47, 062106.Google Scholar

[BHM10] S., Bravyi, M., Hastings, and S., Michalakis. 2010. Topological quantum order: Stability under local perturbations. J. Math. Phys., 51, 093512.Google Scholar

[BPT10] S., Bravyi, D., Poulin, and B., Terhal. 2010. Tradeoffs for reliable quantum information storage in 2D systems. Phys. Rev. Lett., 104, 50503.Google Scholar

[BTL10] S., Bravyi, B. M., Terhal, and B., Leemhuis. 2010. Majorana fermion codes. New J. Phys., 12, 083039.Google Scholar

[BDN+04] M. J., Bremner, J. L., Dodd, M. A., Nielsen, and D., Bacon. 2004. Fungible dynamics: There are only two types of entangling multiple-qubit interactions. Phys. Rev. A, 69, 012313.Google Scholar

[BBN05] M. J., Bremner, D., Bacon, and M. A., Nielsen. 2005. Simulating Hamiltonian dynamics using many-qubit Hamiltonians and local unitary control. Phys. Rev. A, 71, 052312.Google Scholar

[BP02] H.-P., Breuer and F., Petruccione. 2002. The Theory of Open Quantum Systems. Oxford: Oxford University Press.Google Scholar

[BBP04] H.-P., Breuer, D., Burgarth, and F., Petruccione. 2004. Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques. Phys. Rev. B, 70, 045323.Google Scholar

[BE93] H.-J., Briegel and B.-G., Englert. 1993. Quantum optical master equations: The use of damping bases. Phys. Rev. A, 47, 3311.Google Scholar

[B02b] T. A., Brun. 2002. A simple model of quantum trajectories. Am.J.Phys., 70, 719.Google Scholar

[BDH06a] T. A., Brun, I., Devetak, and M.-H. Hsieh. 2006. Catalytic quantum error correction. eprint arXiv:quant-ph/0608027.Google Scholar

[BDH06b] T. A., Brun, I., Devetak, and M.-H., Hsieh. 2006. Correcting quantum errors with entanglement. Science, 314, 436.Google Scholar

[BL07] D., Bruss and G., Leuchs (eds.). 2007. Lectures on Quantum Information. Berlin: Wiley-VCH.

[BF04] H., Bruus and K., Flensberg. 2004. Many-Body Quantum Theory in Condensed Matter Physics. Oxford: Oxford University Press.Google Scholar

[BLD99] G., Burkard, D., Loss, and D. P., DiVincenzo. 1999. Coupled quantum dots as quantum gates. Phys. Rev. B, 59, 2070.Google Scholar

[BL02a] M. S., Byrd and D. A., Lidar. 2002. Comprehensive encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing. Phys. Rev. Lett., 89, 047901.Google Scholar

[BL02b] M., Byrd and D., Lidar. 2002. Bang-bang operations from a geometric perspective. Quant. Inf. Proc., 1, 19.Google Scholar

[BLN95] R. H., Byrd, P., Lu, and J., Nocedal. 1995. A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Statist. Comput., 16, 1190.Google Scholar

[CS96] A. R., Calderbank and P. W., Shor. 1996. Good quantum error-correcting codes exist. Phys. Rev. A, 54, 1098.Google Scholar

[CRS+97] A. R., Calderbank, E. M., Rains, P. W., Shor, and N. J. A., Sloane. 1997. Quantum error correction and orthogonal geometry. Phys. Rev. Lett., 78, 405.Google Scholar

[CRS+98] A. R., Calderbank, E. M., Rains, P. W., Shor, and N. J. A., Sloane. 1998. Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory, 44, 1369.Google Scholar

[COT07] T., Camara, H., Ollivier, and J.-P., Tillich. 2007. A class of quantum LDPC codes: Construction and performances under iterative decoding. ISIT, p. 811.Google Scholar

[C93] H. J., Carmichael. 1993. An Open System Approach to Quantum Optics. Berlin: Springer.Google Scholar

[CP54] H. Y., Carr and E. M., Purcell. 1954. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev., 94, 630.Google Scholar

[C99] C. M., Caves. 1999. Quantum error correction and reversible operations. J. Super-conductivity, 12, 707.Google Scholar

[CLG08] B. A., Chase, A. J., Landahl, and J. M., Geremia. 2008. Efficient feedback controllers for continuous-time quantum error correction. Phys. Rev. A., 77, 032304.Google Scholar

[CL10] K., Chen and R.-B., Liu. 2010. Dynamical decoupling for a qubit in telegraphlike noises. Phys. Rev. A, 82, 052324.Google Scholar

[C07] P., Chen. 2007. Dynamical decoupling induced renormalization of the non-Markovian dynamics. Phys. Rev. A, 75, 062301.Google Scholar

[CZC08] X., Chen, B., Zeng, and I. L., Chuang. 2008. Nonbinary codeword-stabilized quantum codes. Phys. Rev. A, 78, 062315.Google Scholar

[CZZ+06] Y.-A., Chen, A.-N., Zhang, Z., Zhao, X.-Q., Zhou, and J.-W., Pan. 2006. Experimental quantum error rejection for quantum communication. Phys. Rev. Lett., 96, 220504.Google Scholar

[CLS+04] J., Chiaverini, D., Leibfried, T., Schaetz, M. D., Barrett, R. B., Blakestad, J., Britton, W. M., Itano, J. D., Jost, E., Knill, C., Langer, R., Ozeri, and D. J., Wineland. 2004. Realization of quantum error correction. Nature, 432, 602.Google Scholar

[CTS+05] L., Childress, J. M., Taylor, A. S., Sorensen, and M. D., Lukin. 2005. Fault-tolerant quantum repeaters with minimal physical resources and implementations based on single-photon emitters. Phys. Rev. A, 72, 052330.Google Scholar

[CDT+06] L., Childress, M. G., Dutt, J., Taylor, A., Zibrov, F., Jelezko, J., Wrachtrup, P. R., Hemmer, and M. D., Lukin. 2006. Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science, 314, 281.Google Scholar

[CLV04] A. M., Childs, D. W., Leung, and G., Vidal. 2004. Reversible simulation of bipartite product Hamiltonians. IEEE Trans. Inf. Theory, 50, 1189.Google Scholar

[CLN05] A. M., Childs, D. W., Leung, and M. A., Nielsen. 2005. Unified derivations of measurement-based schemes for quantum computation. Phys. Rev. A, 71, 032318.Google Scholar

[CLP07] A. M., Childs, A. J., Landahl, and P. A., Parrilo. 2007. Quantum algorithms for the ordered search problem via semidefinite programming. Phys. Rev. A, 75, 032335.Google Scholar

[CNH+03] I., Chiorescu, Y., Nakamura, C., Harmans, and J., Mooij. 2003. Coherent quantum dynamics of a superconducting flux qubit. Science, 299, 1869.Google Scholar

[C74] M.-D., Choi. 1974. A Schwarz inequality for positive linear maps on C*-algebras. Illinois J. Math., 18, 565.Google Scholar

[C75] M.-D., Choi. 1975. Completely positive linear maps on complex matrices. Lin. Alg. Appl., 10, 285.Google Scholar

[CK06] M.-D., Choi and D. W., Kribs. 2006. Method to find quantum noiseless subsystems. Phys. Rev. Lett., 96, 050501.Google Scholar

[CJK09] M.-D., Choi, N., Johnston, and D. W., Kribs. 2009. The multiplicative domain in quantum error correction. J. Phys. A, 42, 245303.Google Scholar

[CK10] D., Chruścináki and A., Kossakowski. 2010. Non-Markovian quantum dynamics: Local versus nonlocal. Phys. Rev. Lett., 104, 070406.Google Scholar

[CCS+09] I., Chuang, A., Cross, G., Smith, J., Smolin, and B., Zeng. 2009. Codeword stabilized quantum codes: Algorithms and structure. J. Math. Phys., 50, 042109.Google Scholar

[CEH+99] J. I., Cirac, A. K., Ekert, S. F., Huelga, and C., Macchiavello. 1999. Distributed quantum computation over noisy channels. Phys. Rev. A, 59, 4249.Google Scholar

[CBK10] J., Clausen, G., Bensky, and G., Kurizki. 2010. Bath-optimized minimal-energy protection of quantum operations from decoherence. Phys. Rev. Lett., 104, 040401.Google Scholar

[CSG.-B04] J. P., Clemens, S., Siddiqui, and J., Gea-Banacloche. 2004. Quantum error correction against correlated noise. Phys. Rev. A, 70, 069902.Google Scholar

[CB97] R., Cleve and H., Buhrman. 1997. Substituting quantum entanglement for communication. Phys. Rev. A, 56, 1201.Google Scholar

[CG97] R., Cleve and D., Gottesman. 1997. Efficient computations of encodings for quantum error correction. Phys.Rev.A, 56, 76.Google Scholar

[CGL99] R., Cleve, D., Gottesman, and H.-K., Lo. 1999. How to share a quantum secret. Phys. Rev. Lett., 83, 648.Google Scholar

[CEL99] G., Cohen, S., Encheva, and S., Litsyn. 1999. On binary constructions of quantum codes. IEEE Trans. Inf. Theory, 45, 2495.Google Scholar

[CD96] C. J., Colbourn and J. H., Dinitz (eds.). 1996. The CRC Handbook of Combinatorial Designs. Boca Raton: CRC Press.

[CP02] D., Collins and S., Popescu. 2002. Classical analog of entanglement. Phys. Rev. A, 65, 032321.Google Scholar

[CR99] W., Cook and A., Rohe. 1999. Computing minimum-weight perfect matchings. INFORMS J. Comput., 11, 138.Google Scholar

[CMG90] D. G., Cory, J. B., Miller, and A. N., Garroway. 1990. Time-suspension multiple-pulse sequences: Applications to solid-state imaging. J. Magn. Reson., 90, 205.Google Scholar

[CFH97] D. G., Cory, A. F., Fahmy, and T. F., Havel. 1997. Ensemble quantum computing by NMR spectroscopy. Proc. Natl. Acad. Sci. USA, 94, 1634.Google Scholar

[CPM+98] D. G., Cory, M. D., Price, W., Maas, E., Knill, R., Laflamme, W. H., Zurek, T. F., Havel, and S. S., Somaroo. 1998. Experimental quantum error correction. Phys. Rev. Lett., 81, 2152.Google Scholar

[CLK+00] D. G., Cory, R., Laflamme, E., Knill, L., Viola, T. F., Havel, N., Boulant, G., Boutis, E. M., Fortunato, S., Lloyd, R., Martinez, C., Negrevergne, Y., Sharf, G., Teklemariam, Y. S., Weinstein, and W. H., Zurek. 2000. NMR based quantum information processing: Achievements and prospects. Fortschr. Phys., 48, 875.Google Scholar

[CT91] T. M., Cover and J. A., Thomas. 1991. Elements of Information Theory. New York: Wiley.Google Scholar

[CSS+09] A., Cross, G., Smith, J. A., Smolin, and B., Zeng. 2009. Codewords stabilized quantum codes. IEEE Trans. Inf. Theory, 55, 433.Google Scholar

[CPZ05] F. M., Cucchietti, J. P., Paz, and W. H., Zurek. 2005. Decoherence from spin environments. Phys. Rev. A, 72, 052113.Google Scholar

[CFK+87] H., Cycon, R., Froese, W., Kirsch, and B., Simon. 1987. Schrodinger Operators with Applications to Quantum Mechanics and Global Geometry. Berlin: Springer.Google Scholar

[CLN+08] L., Cywiński, R. M., Lutchyn, C. P., Nave, and S. Das, Sarma. 2008. How to enhance dephasing time in superconducting qubits. Phys. Rev. B, 77, 174509.Google Scholar

[DVB10] B., Dakić, V., Vedral, and Č., Brukner. 2010. Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett., 105, 190502.Google Scholar

[D07] D., D'Alessandro. 2007. Introduction to Quantum Control and Dynamics. Boca Raton: CRC Press.Google Scholar

[DCM92] J., Dalibard, Y., Castin, and K., Mølmer. 1992. Wave-function approach to dissipative processes in quantum optics. Phys. Rev. Lett., 68, 580.Google Scholar

[DLG+09] S., Damodarakurup, M., Lucamarini, G. D., Giuseppe, D., Vitali, and P., Tombesi. 2009. Experimental inhibition of decoherence on flying qubits via bang-bang control. Phys. Rev. Lett., 103, 040502.Google Scholar

[DL01] G. M., D'Ariano and P. Lo, Presti. 2001. Optimal nonuniversally covariant cloning. Phys. Rev. A, 64, 042308.Google Scholar

[DKS+07] G., D'Ariano, D., Kretschmann, D., Schlingemann, and R., Werner. 2007. Reexamination of quantum bit commitment: The possible and the impossible. Phys. Rev. A, 76, 032328.Google Scholar

[D96] K. R., Davidson. 1996. C*-Algebras by Example. Providence: American Mathematical Society.Google Scholar

[D74] E., Davies. 1974. Markovian Master Equations. Commun. Math. Phys., 39, 91.Google Scholar

[dWR+10] G., de Lange, Z. H., Wang, D., Ristè, V. V., Dobrovitski, and R., Hanson. 2010. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science, 330, 60.Google Scholar

[dRD+11] G., de Lange, D., Ristè, V. V., Dobrovitski, and R., Hanson. 2011. Single-spin magnetometry with multipulse sensing sequences. Phys. Rev. Lett., 106, 080802.Google Scholar

[d67] J., de Pillis. 1967. Linear transformations which preserve Hermitian and positive semidefinite operations. Pacific J. Math., 23, 129.Google Scholar

[D86] W., de Launey. 1986. A survey of generalized Hadamard matrices and difference matrices D(K, λ G) with large k. Utilitas Math., 30, 5.Google Scholar

[DKL+02] E., Dennis, A., Kitaev, A., Landahl, and J., Preskill. 2002. Topological quantum memory. J. Math. Phys., 43, 4452.Google Scholar

[D05] I., Devetak. 2005. The private classical capacity and quantum capacity of a quantum channel. IEEE Trans. Inf. Theory, 51, 44.Google Scholar

[DY08] I., Devetak and J., Yard. 2008. Exact cost of redistributing multipartite quantum states. Phys. Rev. Lett., 100, 230501.Google Scholar

[DHW04] I., Devetak, A. W., Harrow, and A., Winter. 2004. A family of quantum protocols. Phys. Rev. Lett., 93, 230504.Google Scholar

[DHW08] I., Devetak, A. W., Harrow, and A., Winter. 2008. A resource framework for quantum Shannon theory. IEEE Trans. Inf. Theory, 54, 4587.Google Scholar

[DGI+07] S. J., Devitt, A. D., Greentree, R., Ionicioiu, J. L., O'Brien, W. J., Munro, and L. C. L., Hollenberg. 2007. The photonic module: An on-demand resource for photonic entanglement. Phys. Rev. A, 76, 052312.Google Scholar

[DGR06] D., Dhar, L. K., Grover, and S. M., Roy. 2006. Preserving quantum states using inverting pulses: A super-Zeno effect. Phys. Rev. Lett., 96, 100405.Google Scholar

[D54] R., Dicke. 1954. Coherence in spontaneous radiation processes. Phys. Rev., 93, 99.Google Scholar

[D95] D. P., DiVincenzo. 1995. Quantum computation. Science, 270, 255.Google Scholar

[D00] D. P., DiVincenzo. 2000. The physical implementation of quantum computation. Fortschr. Phys., 48, 771.Google Scholar

[DA07] D. P., DiVincenzo and P., Aliferis. 2007. Effective fault-tolerant quantum computation with slow measurements. Phys. Rev. Lett., 98, 020501.Google Scholar

[DNB+02] J. L., Dodd, M. A., Nielsen, M. J., Bremner, and R. T., Thew. 2002. Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries. Phys. Rev. A, 65, 040301.Google Scholar

[DPS05] A. C., Doherty, P. A., Parrilo, and F. M., Spedalieri. 2005. Detecting multipartite entanglement. Phys.Rev.A, 71, 03233.Google Scholar

[DHR02] M. J., Donald, M., Horodecki, and O., Rudolph. 2002. The uniqueness theorem for entanglement measures. J. Math. Phys., 43, 4252.Google Scholar

[DRZ+09] J., Du, X., Rong, N., Zhao, Y., Wang, J., Yang, and R.-B., Liu. 2009. Preserving electron spin coherence in solids by optimal dynamical decoupling. Nature, 461, 1265.Google Scholar

[DG97] L. M., Duan and G. C., Guo. 1997. Preserving coherence in quantum computation by pairing quantum bits. Phys. Rev. Lett., 79, 1953.Google Scholar

[DG98a] L.-M., Duan and G.-C., Guo. 1998. Optimal quantum codes for preventing collective amplitude damping. Phys. Rev. A, 58, 3491.Google Scholar

[DG98b] L. M., Duan and G. C., Guo. 1998. Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment. Phys. Rev. A, 57, 737.Google Scholar

[DG99] L.-M., Duan and G.-C., Guo. 1999. Suppressing environmental noise in quantum computation through pulse control. Phys. Lett. A, 261, 139.Google Scholar

[DCZ01] L.-M., Duan, J., Cirac, and P., Zoller. 2001. Geometric manipulation of trapped ions for quantum computation. Science, 292, 1695.Google Scholar

[D.-CP10] G., Duclos-Cianci and D., Poulin. 2010. Fast decoders for topological quantum codes. Phys. Rev. Lett., 104, 050504.Google Scholar

[DB03] W., Dür and H.-J., Briegel. 2003. Entanglement purification for quantum computation. Phys. Rev. Lett., 90, 067901.Google Scholar

[DB07] W., Dür and H. J., Briegel. 2007. Entanglement purification and quantum error correction. Rep. Prog. Phys., 70, 1381.Google Scholar

[DVC+01] W., Dür, G., Vidal, J. I., Cirac, N., Linden, and S., Popescu. 2001. Entanglement capabilities of non-local Hamiltonians. Phys. Rev. Lett., 87, 137901.Google Scholar

[DMO01] M., Durdevich, H. E., Makaruk, and R., Owczarek. 2001. Generalized noiseless quantum codes utilizing quantum enveloping algebras. J. Phys. A, 34, 1423.Google Scholar

[DCJ+07] M. V. G., Dutt, L., Childress, L., Jiang, E., Togan, J., Maze, F., Jelezko, A. S., Zibrov, P. R., Hemmer, and M. D., Lukin. 2007. Quantum register based on individual electronic and nuclear spin qubits in diamond. Science, 316, 1312.Google Scholar

[E65] J., Edmonds. 1965. Paths, trees, and flowers. Can. J. Math., 17, 449.Google Scholar

[EP03] J., Eisert and M. B., Plenio. 2003. Introduction to the basics of entanglement theory in continuous-variable systems. Int. J. Quant. Inf., 1, 479.Google Scholar

[E91] A. K., Ekert. 1991. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett., 67, 661.Google Scholar

[EM96] A., Ekert and C., Macchiavello. 1996. Error correction in quantum communication. Phys. Rev. Lett., 77, 2585.Google Scholar

[E03a] Y. C., Eldar. 2003. Mixed-quantum-state detection with inconclusive results. Phys. Rev. A, 67, 042309.Google Scholar

[E03b] Y. C., Eldar. 2003. A semidefinite programming approach to optimal unambiguous discrimination of quantum states. IEEE Trans. Inf. Theory, 49, 446.Google Scholar

[EMV03] Y., Eldar, A., Megretski, and G., Verghese. 2003. Designing optimal quantum detectors via semidefinite programming. IEEE Trans. Inf. Theory, 49, 1007.Google Scholar

[ESH04] Y. C., Eldar, M., Stojnic, and B., Hassibi. 2004. Optimal quantum detectors for unambiguous detection of mixed states. Phys. Rev. A, 69, 062318.Google Scholar

[EBW94] R., Ernst, G., Bodenhausen, and A., Wokaun. 1994. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Oxford: Oxford University Press.Google Scholar

[FLP04] P., Facchi, D. A., Lidar, and S., Pascazio. 2004. Unification of dynamical decoupling and the quantum zeno effect. Phys. Rev. A, 69, 032314.Google Scholar

[FI06] L., Faoro and L. B., Ioffe. 2006. Quantum two level systems and Kondo-like traps as possible sources of decoherence in superconducting qubits. Phys. Rev. Lett., 96, 047001.Google Scholar

[FI08] L., Faoro and L. B., Ioffe. 2008. Microscopic origin of low-frequency flux noise in Josephson circuits. Phys. Rev. Lett., 100, 227005.Google Scholar

[FV04] L., Faoro and L., Viola. 2004. Dynamical suppression of 1/f noise processes in qubit systems. Phys. Rev. Lett., 92, 117905.Google Scholar

[F01] D., Farenick. 2001. Algebras of Linear Transformations. New York: Springer-Verlag.Google Scholar

[FGG+00] E., Farhi, J., Goldstone, S., Gutmann, and M., Sipser. 2000. Quantum computation by adiabatic evolution. eprint arXiv:quant-ph/0001106.Google Scholar

[FCY+04] D., Fattal, T. S., Cubitt, Y., Yamamoto, S., Bravyi, and I. L., Chuang. 2004. Entanglement in the stabilizer formalism. eprint arXiv:quant-ph/0406168.Google Scholar

[FHB01] M., Fazel, H., Hindi, and S., Boyd. 2001. A rank minimization heuristic with application to minimum order system approximation. American Control Conference, 2001, 6, 4734.Google Scholar

[FHB03] M., Fazel, H., Hindi, and S., Boyd. 2003. Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices. American Control Conference, 2003, 3, 2156.Google Scholar

[FHB04] M., Fazel, H., Hindi, and S., Boyd. 2004. Rank minimization and applications in system theory. American Control Conference, 2004, 4, 3273.Google Scholar

[F82] R. P., Feynman. 1982. Simulating physics with computers. Int. J. Theor. Phys., 21, 467.Google Scholar

[FMA05] R., Filip, P., Marek, and U. L., Andersen. 2005. Measurement-induced continuous-variable quantum interactions. Phys. Rev. A, 71, 042308.Google Scholar

[F00] S. D., Filippo. 2000. Quantum computation using decoherence-free states of the physical operator algebra. Phys. Rev. A, 62, 052307.Google Scholar

[FSW07] A. S., Fletcher, P. W., Shor, and M. Z., Win. 2007. Optimum quantum error recovery using semidefinite programming. Phys. Rev. A, 75, 012338.Google Scholar

[FSW08] A. S., Fletcher, P. W., Shor, and M. Z., Win. 2008. Structured near-optimal channel-adapted quantum error recovery. Phys.Rev.A, 77, 012320.Google Scholar

[FC07] G., Forney and D., Costello. 2007. Channel coding: The road to channel capacity. Proc. IEEE, 95, 1150.Google Scholar

[FG05] G. D., Forney and S., Guha. 2005. Simple rate-1/3 convolutional and tail-biting quantum error-correcting codes. Proceedings of the IEEE International Symposium on Information Theory, p. 1028.Google Scholar

[FGG07] G. D., Forney, M., Grassl, and S., Guha. 2007. Convolutional and tail-biting quantum error-correcting codes. IEEE Trans. Inf. Theory, 53, 865.Google Scholar

[FVH+02] E. M., Fortunato, L., Viola, J., Hodges, G., Teklemariam, and D. G., Cory. 2002. Implementation of universal control on a decoherence-free qubit. New J. Phys., 4, 5.1.Google Scholar

[FPB+02] E., Fortunato, M., Pravia, N., Boulant, T., Havel, and D., Cory. 2002. Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing. J. Chem. Phys., 116, 7599.Google Scholar

[FG09] A. G., Fowler and K., Goyal. 2009. Topological cluster state quantum computing. Quant. Inf. Comput., 9, 721.Google Scholar

[FWM+12] A. G., Fowler, A. C., Whiteside, A. L., McInnes, and A., Rabbani. 2012. Topological code Autotune. eprint arXiv:1202.6111.Google Scholar

[FWH12a] A. G., Fowler, A. C., Whiteside, and L. C. L., Hollenberg. 2012. Towards practical classical processing for the surface code. Phys. Rev. Lett., 108, 180501.Google Scholar

[FWH12b] A. G., Fowler, A. C., Whiteside, and L. C. L., Hollenberg. 2012. Towards practical classical processing for the surface code: timing analysis. Phys. Rev. A, 86, 042313.Google Scholar

[FSL05] E., Fraval, M. J., Sellars, and J. J., Longdell. 2005. Dynamic decoherence control of a solid-state nuclear quadrupole qubit. Phys. Rev. Lett., 95, 030506.Google Scholar

[FM01] M., Freedman and D., Meyer. 2001. Projective plane and planar quantum codes. Found. Comp. Math., 1, 325.Google Scholar

[FKL+03] M., Freedman, A., Kitaev, M., Larsen, and Z., Wang. 2003. Topological quantum computation. Bull. Amer. Math. Soc., 40, 31.Google Scholar

[FKL80] R., Freeman, S. P., Kempsell, and M. H., Levitt. 1980. Radio-frequency pulse sequences which compensate their own imperfections. J. Magn. Reson, 38, 453.Google Scholar

[FKM+04] J., Furrer, F., Kramer, J. P., Marino, S. J., Glaser, and B., Luy. 2004. Homonuclear Hartmann-Hahn transfer with reduced relaxation losses by use of the MOCCAXY16 multiple pulse sequence. J. Magn. Reson, 166, 39.Google Scholar

[G83] P., Gács. 1983. Reliable computation with cellular automata. Proceedings 15th Annual ACM Symposium on Theory of Computing. New York: ACM Press, p. 32.Google Scholar

[G01a] P., Gács. 2001. Reliable cellular automata with self-organization. J. Stat. Phys., 103, 45.Google Scholar

[G05] P., Gács. 2005. Reliable computation. Online at Gács' website at Boston University. www.cs.bu.edu/~gacs/.Google Scholar

[G08] F., Gaitan. 2008. Quantum Error Correction and Fault Tolerant Quantum Computing. Boca Raton: CRC Press.Google Scholar

[G63] R. G., Gallager. 1963. Low Density Parity Check Codes. Cambridge, MA: MIT Press.Google Scholar

[GFR+09] W., Gao, A. G., Fowler, R., Raussendorf, X., Yao, H., Lu, P., Xu, C., Lu, C., Peng, Y., Deng, Z., Chen, and J., Pan. 2009. Experimental demonstration of topological error correction. eprint arXiv:0905.1542.Google Scholar

[GZ04] C. W., Gardiner and P., Zoller. 2004. Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics. 3rd edn. Berlin, Heidelberg: Springer-Verlag.Google Scholar

[GJ79] M. R., Garey and D. S., Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W. H. Freeman & Co.Google Scholar

[G76] M., Gaudin. 1976. Diagonalisation d'une classe d'hamiltoniens de spin. J. Physique, 37, 1087.Google Scholar

[GC97] N. A., Gershenfeld and I. L., Chuang. 1997. Bulk spin-resonance quantum computation. Science, 275, 350.Google Scholar

[G.-S02] S., Gheorghiu-Svirschevski. 2002. Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment. Phys. Rev. A, 66, 032101.Google Scholar

[GKL+03] R. M., Gingrich, P., Kok, H., Lee, F., Vatan, and J. P., Dowling. 2003. All linear optical quantum memory based on quantum error correction. Phys. Rev. Lett., 91, 217901.Google Scholar

[GLM+03] V., Giovannetti, S., Lloyd, L., Maccone, and P. W., Shor. 2003. Broadband channel capacities. Phys. Rev. A, 68, 062323.Google Scholar

[GGL+04] V., Giovannetti, S., Guha, S., Lloyd, L., Maccone, J. H., Shapiro, and H. P., Yuen. 2004. Classical capacity of the lossy bosonic channel: The exact solution. Phys. Rev. Lett., 92, 027902.Google Scholar

[G74] J.-M., Goethals. 1974. Two families of nonlinear binary codes. Electron. Lett., 10, 471.Google Scholar

[GNT98] A. O., Gogolin, A. A., Nersesyan, and A. M., Tsvelik. 1998. Bosonization and Strongly Correlated Systems. Cambridge: Cambridge University Press.Google Scholar

[GKL08] G., Gordon, G., Kurizki, and D., Lidar. 2008. Optimal dynamical decoherence control of a qubit. Phys. Rev. Lett., 101, 010403.Google Scholar

[GKS76] V., Gorini, A., Kossakowski, and E., Sudarshan. 1976. Completely positive dynamical semigroups of N-level systems. J. Math. Phys., 17, 821.Google Scholar

[G96a] D., Gottesman. 1996. Class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A, 54, 1862.Google Scholar

[G97a] D., Gottesman. 1997. Stabilizer Codes and Quantum Error Correction. Ph.D. thesis, California Institute of Technology. eprint arXiv:quant-ph/9705052.Google Scholar

[G98] D., Gottesman. 1998. Theory of fault-tolerant quantum computation. Phys. Rev. A, 57, 127.Google Scholar

[G99] D., Gottesman. 1999. Fault-tolerant quantum computation with higher-dimensional systems. Chaos Solitons Fractals, 10, 1749.Google Scholar

[G00] D., Gottesman. 2000. Fault-tolerant quantum computation with local gates. J. Mod. Optics, 47, 333.Google Scholar

[G09] D., Gottesman. 2009. An introduction to quantum error correction and fault-tolerant quantum computation. eprint arXiv:0904.2557.Google Scholar

[GC99] D., Gottesman and I., Chuang. 1999. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402, 390.Google Scholar

[GKP01] D., Gottesman, A., Kitaev, and J., Preskill. 2001. Encoding a qubit in an oscillator. Phys. Rev. A, 64, 012310.Google Scholar

[GB97] M., Grassl and T., Beth. 1997. A note on non-additive quantum codes. eprint arXiv:quant-ph/9703016.Google Scholar

[GB99] M., Grassl and T., Beth. 1999. Quantum BCH codes. Proceedings Xth International Symposium on Theoretical Electrical Engineering, Magdeburg, p. 207.Google Scholar

[GR06a] M., Grassl and M., Rötteler. 2006. Noncatastrophic encoders and encoder inverses for quantum convolutional codes. Proceedings of the IEEE International Symposium on Information Theory, p. 1109.Google Scholar

[GR06b] M., Grassl and M., Rotteler. 2006. Quantum convolutional codes: Encoders and structural properties. Proceedings of the Forty-Fourth Annual Allerton Conference, p. 510.Google Scholar

[GR07] M., Grassl and M., Rotteler. 2007. Constructions of quantum convolutional codes. Proceedings of the IEEE International Symposium on Information Theory, p. 816.Google Scholar

[GR08a] M., Grassl and M., Rötteler. 2008. Non-additive quantum codes from Goethals and Preparata codes. Proceedings of the IEEE Information Theory Workshop (ITW 08), p. 396.Google Scholar

[GR08b] M., Grassl and M., Rötteler. 2008. Quantum Goethals-Preparata codes. Proceedings of the IEEE International Symposium on Information Theory, p. 300.Google Scholar

[GBP97] M., Grassl, T., Beth, and T., Pellizzari. 1997. Codes for the quantum erasure channel. Phys.Rev.A, 56, 33.Google Scholar

[GKR02] M., Grassl, A., Klappenecker, and M., Rötteler. 2002. Graphs, quadratic forms, and quantum codes. Proceedings of the IEEE International Symposium on Information Theory, p. 45.Google Scholar

[GRB03] M., Grassl, M., Rötteler, and T., Beth. 2003. Efficient quantum circuits for nonqubit quantum error-correcting codes. Int. J.Found. Comput. Sci., 14, 757.Google Scholar

[GBR04] M., Grassl, T., Beth, and M., Rötteler. 2004. On optimal quantum codes. Int. J. Quant. Inf., 2, 757.Google Scholar

[GSS+09] M., Grassl, P., Shor, G., Smith, J., Smolin, and B., Zeng. 2009. Generalized concatenated quantum codes. Phys. Rev. A, 79, 050306(R).Google Scholar

[G01b] L. F., Gray. 2001. A reader's guide to Gacs's “positive rates” paper. Online at Gray's website at the University of Minnesota. www.math.umn.edu/~gray/.Google Scholar

[GPW99] M., Grifoni, E., Paladino, and U., Weiss. 1999. Dissipation, decoherence and preparation effects in the spin-boson system. Eur. Phys. J. B, 10, 719.Google Scholar

[G96b] L. K., Grover. 1996. A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC), p. 212.Google Scholar

[G97b] L. K., Grover. 1997. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett., 79, 325.Google Scholar

[GSE08] S., Guha, J. H., Shapiro, and B. I., Erkmen. 2008. Capacity of the bosonic wiretap channel and the entropy photon-number inequality. Proceedings of the 2008 International Symposium on Information Theory, p. 91.Google Scholar

[GBC90] T., Gullion, D. B., Baker, and M. S., Conradi. 1990. New, compensated Carr-Purcell sequences. J. Magn. Reson., 89, 479.Google Scholar

[H11] J., Haah. 2011. Local stabilizer codes in three dimensions without string logical operators. Phys. Rev. A, 83, 042330.Google Scholar

[H76] U., Haeberlen. 1976. High Resolution NMR in Solids: Selective Averaging. New York: Academic Press.Google Scholar

[HW68] U., Haeberlen and J. S., Waugh. 1968. Coherent averaging effect in magnetic resonance. Phys. Rev., 175, 453.Google Scholar

[HJ02] G. A., Hagedorn and A., Joye. 2002. Elementary exponential error estimates for the adiabatic approximation. J. Math. Anal. Appl., 267, 235.Google Scholar

[HI07] M., Hagiwara and H., Imai. 2007. Quantum quasi-cyclic LDPC codes. Proceedings of the IEEE International Symposium on Information Theory, p. 806.Google Scholar

[H50] E. L., Hahn. 1950. Spin echoes. Phys. Rev., 80, 580.Google Scholar

[HSK+98] B., Ham, M., Shahriar, M., Kim, and P., Hemmer. 1998. Spin coherence excitation and rephasing with optically shelved atoms. Phys. Rev. B, 58, R11825.Google Scholar

[HKC+94] A. R., Hammons Jr., P. V., Kumar, A. R., Calderbank, N. J. A., Sloane, and P., Solé. 1994. The ℤ4-Linearity of Kerdock, Preparata, Goethals, and related codes. IEEE Trans. Inf. Theory, 40, 301.Google Scholar

[HP01] J., Harrington and J., Preskill. 2001. Achievable rates for the Gaussian quantum channel. Phys. Rev. A, 64, 062301.Google Scholar

[H02] A., Hatcher. 2002. Algebraic Topology. Cambridge: Cambridge University Press.Google Scholar

[H03] T. F., Havel. 2003. Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups. J. Math. Phys., 44, 534.Google Scholar

[H07] M., Hayashi. 2007. Upper bounds of eavesdropper's performances in finite-length code with the decoy method. Phys. Rev. A, 76, 012329.Google Scholar

[HHW+08] P., Hayden, M., Horodecki, A., Winter, and J., Yard. 2008. A decoupling approach to the quantum capacity. Open Syst. Inf. Dynam., 15, 7.Google Scholar

[HSW08] P., Hayden, P. W., Shor, and A., Winter. 2008. Random quantum codes from Gaussian ensembles and an uncertainty relation. Open Syst. Inf. Dynam., 15, 71.Google Scholar

[HCD+11] D., Hayes, S. M., Clark, S., Debnath, D., Hucul, Q., Quraishi, and C. M., Monroe. 2011. Coherent error suppression in spin-dependent force quantum gates. eprint arXiv:1104.1347.Google Scholar

[HKV+11] D., Hayes, K., Khodjasteh, L., Viola, and M. J., Biercuk. 2011. Reducing sequencing complexity in quantum dynamical error suppression by Walsh modulation. eprint arXiv:1109.6002.Google Scholar

[HSS99] A. S., Hedayat, N. J. A., Sloane, and J., Stufken. 1999. Orthogonal Arrays. Springer Series in Statistics. New York: Springer.Google Scholar

[H90] F. B., Hergert. 1990. On the Delsarte-Goethals codes and their formal duals. Discrete Math., 83, 249.Google Scholar

[H93] A. C., Hewson. 1993. The Kondo Problem. Cambridge: Cambridge University Press.Google Scholar

[H73] R., Hill. 1973. Linear transformations which preserve Hermitian matrices. Linear Algebr. Appl., 6, 257.Google Scholar

[HVD10] T. E., Hodgson, L., Viola, and I., D'Amico. 2010. Towards optimized suppression of dephasing in systems subject to pulse timing constraints. Phys. Rev. A, 81, 062321.Google Scholar

[HDW+04] L. C. L., Hollenberg, A., Dzurak, C., Wellard, A., Hamilton, D., Reilly, G., Milburn, and R., Clark. 2004. Charge-based quantum computing using single donors in semiconductors. Phys. Rev. B, 69, 113301.Google Scholar

[HOW05] M., Horodecki, J., Oppenheim, and A., Winter. 2005. Partial quantum information. Nature, 436, 673.Google Scholar

[HOW07] M., Horodecki, J., Oppenheim, and A., Winter. 2007. Quantum state merging and negative information. Commun. Math. Phys., 269, 107.Google Scholar

[HLW08] M., Horodecki, S., Lloyd, and A., Winter. 2008. Quantum coding theorem from privacy and distinguishability. Open Syst. Inf. Dynam., 15, 47.Google Scholar

[HHH+09] R., Horodecki, P., Horodecki, M., Horodecki, and K., Horodecki. 2009. Quantum entanglement. Rev. Mod. Phys., 81, 865.Google Scholar

[HH.-KW10] M., Houshmand, S., Hosseini-Khayat, and M., Wilde. 2010. Minimal memory requirements for pearl-necklace encoders of quantum convolutional codes. IEEE Trans. Comput., PP, 1.Google Scholar

[HH.-KW11] M., Houshmand, S., Hosseini-Khayat, and M. M., Wilde. 2011. Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders. eprint arXiv:1105.0649.Google Scholar

[HW10] M.-H., Hsieh and M. M., Wilde. 2010. Trading classical communication, quantum communication, and entanglement in quantum Shannon theory. IEEE Trans. Inf. Theory, 56, 4705.Google Scholar

[HDB07] M.-H., Hsieh, I., Devetak, and T. A., Brun. 2007. General entanglement-assisted quantum error-correcting codes. Phys. Rev. A, 76, 062313.Google Scholar

[HBD09] M.-H., Hsieh, T. A., Brun, and I., Devetak. 2009. Quantum quasi-cyclic low-density parity-check codes. Phys. Rev. A, 79, 032340.Google Scholar

[HYH11] M.-H., Hsieh, W.-T., Yen, and L.-Y., Hsu. 2011. High performance entanglement-assisted quantum LDPC codes need little entanglement. IEEE Trans. Inf. Theory, 57, 1761.Google Scholar

[HTZ+08] D., Hu, W., Tang, M., Zhao, Q., Chen, S., Yu, and C., Hiap. 2008. Graphical nonbi-nary quantum error-correcting codes. Phys.Rev.A, 78, 012306.Google Scholar

[HP03] W. C., Huffman and V., Pless. 2003. Fundamentals of Error-Correcting Codes. Cambridge: Cambridge University Press.Google Scholar

[IAB+99] A., Imamoglu, D. D., Awschalom, G., Burkard, D. P., DiVincenzo, D., Loss, M. Sherwin, and A., Small. 1999. Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett., 83, 4204.Google Scholar

[I02] A., Iserles. 2002. Expansions that grow on trees. Not. AMS, 49, 430.Google Scholar

[J04] K., Jacobs. 2004. Optimal feedback control for the rapid preparation of a single qubit. Proc. SPIE, 5468, 355.Google Scholar

[JSB+09] E. R., Jenista, A. M., Stokes, R. T., Branca, and W., Warren. 2009. Optimized, unequal pulse spacing in multiple echo sequences improves refocusing in magnetic resonance. J. Chem. Phys., 131, 240510.Google Scholar

[JŘF02] M., Ježek, J., Řeháček, and J., Fiurášek. 2002. Finding optimal strategies for minimum-error quantum-state discrimination. Phys. Rev. A, 65, 060301.Google Scholar

[JI11] L., Jiang and A., Imambekov. 2011. Universal dynamical decoupling of multiqubit states from environment. Phys. Rev. A, 84, 060302.Google Scholar

[JTS+07] L., Jiang, J. M., Taylor, A., Sørensen, and M. D., Lukin. 2007. Distributed quantum computation based on small quantum registers. Phys.Rev.A, 76, 062323.Google Scholar

[JZ99] R., Johannesson and K. S., Zigangirov. 1999. Fundamentals of Convolutional Coding. New York: Wiley-IEEE Press.Google Scholar

[JK99] J. A., Jones and E., Knill. 1999. Efficient refocusing of one-spin and two-spin interactions for NMR quantum computation. J. Magn. Reson., 141, 322.Google Scholar

[JVE+00] J. A., Jones, V., Vedral, A., Ekert, and G., Castagnoli. 2000. Geometric quantum computation using nuclear magnetic resonance. Nature, 403, 869.Google Scholar

[JFS06] S., Jordan, E., Farhi, and P., Shor. 2006. Error-correcting codes for adiabatic quantum computation. Phys. Rev. A, 74, 052322.Google Scholar

[JSS04] T., Jordan, A., Shaji, and E., Sudarshan. 2004. Dynamics of initially entangled open quantum systems. Phys. Rev. A, 70, 052110.Google Scholar

[JP05] P., Jorrand and S., Perdrix. 2005. Unifying quantum computation with projective measurements only and one-way quantum computation. Proceedings SPIE, Quantum Informatics (QI'04), Vol. 5833, p. 44.Google Scholar

[KU98] N., Kahale and R., Urbanke. 1998. On the minimum distance of parallel and serially concatenated codes. Proceedings IEEE International Symposium on Information Theory (ISIT'98), p. 31.Google Scholar

[K05a] A., Kamenev. 2005. Many-body theory of non-equilibrium systems. In H., Bouchiat, Y., Gefen, S., Guron, G., Montambaux, and J., Dalibard (eds.), Nanophysics: Coherence and Transport, Les Houches Summer School Proceedings, Vol. 81, p. 177. Amsterdam: Elsevier.Google Scholar

[KYS08] B. E., Kardynal, Z. L., Yuan, and A. J., Shields. 2008. An avalanche-photodiode-based photon-number-resolving detector. Nature Photonics, 2, 425.Google Scholar

[KBM.-D09] H., Katzgraber, H., Bombin, and M., Martin-Delgado. 2009. Error threshold for color codes and random 3-body ising models. Phys. Rev. Lett., 103, 090501.Google Scholar

[KBA+10] H., Katzgraber, H., Bombin, R., Andrist, and M., Martin-Delgado. 2010. Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group. Phys.Rev.A, 81, 012319.Google Scholar

[KBL+01] J., Kempe, D., Bacon, D. A., Lidar, and K. B., Whaley. 2001. Theory of decoherence-free, fault-tolerant, universal quantum computation. Phys. Rev. A, 63, 042307.Google Scholar

[KBS+09] J., Kerckhoff, L., Bouten, A., Silberfarb, and H., Mabuchi. 2009. Physical model of continuous two-qubit parity measurement in a cavity-QED network. Phys. Rev. A, 79, 024305.Google Scholar

[K09] O., Kern. 2009. Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography. Ph. D. thesis, Technische Universitäat Darmstadt. eprint arXiv:0906.2927.Google Scholar

[KA05] O., Kern and G., Alber. 2005. Controlling quantum systems by embedded dynamical decoupling schemes. Phys. Rev. Lett., 95, 250501.Google Scholar

[KA06] O., Kern and G., Alber. 2006. Selective recoupling and stochastic dynamical decoupling. Phys. Rev. A, 73, 062302.Google Scholar

[KAS05] O., Kern, G., Alber, and D. L., Shepelyansky. 2005. Quantum error correction of coherent errors by randomization. Eur. Phys. J.D, 32, 153.Google Scholar

[KKK+06] A., Ketkar, A., Klappenecker, S., Kumar, and P., Sarvepalli. 2006. Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory, 52, 4892.Google Scholar

[KLG02] A. V., Khaetskii, D., Loss, and L., Glazman. 2002. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett., 88, 186802.Google Scholar

[KL05] K., Khodjasteh and D. A., Lidar. 2005. Fault-tolerant quantum dynamical decoupling. Phys. Rev. Lett., 95, 180501.Google Scholar

[KL07] K., Khodjasteh and D. A., Lidar. 2007. Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences. Phys. Rev. A, 75, 062310.Google Scholar

[KL08] K., Khodjasteh and D. A., Lidar. 2008. Rigorous bounds on the performance of a hybrid Dynamical decoupling—quantum computing scheme. Phys. Rev. A, 78, 012355.Google Scholar

[KV09a] K., Khodjasteh and L., Viola. 2009. Dynamical quantum error correction of unitary operations with bounded controls. Phys. Rev. A, 80, 032314.Google Scholar

[KV09b] K., Khodjasteh and L., Viola. 2009. Dynamically error-corrected gates for universal quantum computation. Phys. Rev. Lett., 101, 080501.Google Scholar

[KLV10] K., Khodjasteh, D. A., Lidar, and L., Viola. 2010. Arbitrarily accurate dynamical control in open quantum systems. Phys. Rev. Lett., 104, 090501.Google Scholar

[KEV11] K., Khodjasteh, T., Erdélyi, and L., Viola. 2011. Limits on preserving quantum coherence using multipulse control. Phys. Rev. A, 83, 020305.Google Scholar

[KDV11] K., Khodjasteh, V. V., Dobrovitski, and L., Viola. 2011. Pointer states via engineered dissipation. Phys. Rev. A, 84, 022336.Google Scholar

[KMW02] D., Kielpinski, C., Monroe, and D., Wineland. 2002. Architecture for a large-scale ion-trap quantum computer. Nature, 417, 709.Google Scholar

[KK05] G., Kimura and A., Kossakowski. 2005. A note on positive maps and classification of states. Open Syst. Inf. Dyn., 12, 207.Google Scholar

[K97a] A., Kitaev. 1997. Quantum computation: Algorithms and error correction. Russ. Math. Surv., 52, 1191.Google Scholar

[K97b] A., Kitaev. 1997. Quantum error correction with imperfect gates. In O., Hirota, A. S., Holevo, and C. M., Caves (eds.), Proceeding of the Third International Conference on Quantum Communication and Measurement. New York: Plenum, p. 181.Google Scholar

[K03a] A., Kitaev. 2003. Fault-tolerant quantum computation by anyons. Ann. Phys., 303, 2.Google Scholar

[KS07] A., Klappenecker and P. K., Sarvepalli. 2007. On subsystem codes beating the quantum Hamming or Singleton bound. Proc. R. Soc. A, 463, 2887.Google Scholar

[KS08] A., Klappenecker and P., Sarvepalli. 2008. Clifford code construction of operator quantum error-correcting codes. IEEE Trans. Inf. Theory, 54, 5760.Google Scholar

[K89] H., Kleinert. 1989. Gauge Fields in Condensed Matter. Singapore; Teaneck, NJ: World Scientific.Google Scholar