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This thesis addresses whether it is possible to build a robust memory device for quantum information.
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Good quantum error-correcting codes exist
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A class of quantum error-correcting codes saturating the quantum hamming bound
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Non-binary unitary error bases and quantum codes (1996)
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Entanglement renormalization
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Entanglement renormalization and topological order
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Anyonic interferometry and protected memories in atomic spin lattices
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URL http://physics.nist.gov/Pubs/SP330/sp330.pdf
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Quantum error correction and orthogonal geometry
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A nonadditive quantum code
Rains, E. M., Hardin, R. H., Shor, P. W. & Sloane, N. J. A · 1997
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Fault-tolerant quantum computation
Preskill, J · 1998
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Quantum error correction via codes over gf(4)
Calderbank, A., Rains, E., Shor, P. & Sloane, N. J. A · 1998
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A theory of fault-tolerant quantum computation
Gottesman, D · 1998
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Güneri, C. & Özbudak, F · 2008
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A class of quantum many-body states that can be efficiently simulated
Vidal, G · 2008
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Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems
Nussinov, Z. & Ortiz, G · 2008
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Fast decoders for topological quantum codes
Duclos-Cianci, G. & Poulin, D · 2009
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Toric-boson model: Toward a topological quantum memory at finite temperature
Hamma, A., Castelnovo, C. & Chamon, C · 2009
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Topological quantum order: stability under local perturbations
Bravyi, S., Hastings, M. & Michalakis, S · 2010
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Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes
Chesi, S., Loss, D., Bravyi, S. & Terhal, B. M · 2010
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Hasan, M. Z. & Kane, C. L · 2010
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On thermal stability of topological qubit in Kitaev’s 4d model
Alicki, R., Horodecki, M., Horodecki, P. & Horodecki, R · 2010
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Framework for classifying logical operators in stabilizer codes
Yoshida, B. & Chuang, I. L · 2010
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Nonlocal quantum information in bipartite quantum error correction
Wilde, M. M. & Fattal, D · 2010
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Quantum convolutional coding with shared entanglement: General structure
Wilde, M. M. & Brun, T. A · 2010
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Chen, X., Gu, Z.-C. & Wen, X.-G · 2010
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Peps as ground states: degeneracy and topology
Schuch, N., Cirac, I. & Perez-Garcia, D · 2010
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In-place algorithm for connected components labeling
Asano, T. & Tanaka, H · 2010
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Self-correcting quantum memory in a thermal environment
Chesi, S., Röthlisberger, B. & Loss, D · 2010
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Thermal states of anyonic systems
Iblisdir, S., Pérez-García, D., Aguado, M. & Pachos, J · 2010
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Topological order at non-zero temperature
Hastings, M. B · 2011
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Feasibility of self-correcting quantum memory and thermal stability of topological order
Yoshida, B · 2011
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On the energy landscape of 3D spin Hamiltonians with topological order
Bravyi, S. & Haah, J · 2011
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Analytic and numerical demonstration of quantum self-correction in the 3D cubic code (2011)
Bravyi, S. & Haah, J · 2011
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Subsystem codes with spatially local generators
Bravyi, S · 2011
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Stability of frustration-free Hamiltonians (2011)
Michalakis, S. & Pytel, J · 2011
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A short proof of stability of topological order under local perturbations
Bravyi, S. & Hastings, M. B · 2011
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Yoshida, B · 2011
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Structure of 2D topological stabilizer codes (2011)
Bombin, H · 2011
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Topological order in an exactly solvable 3D spin model
Bravyi, S., Leemhuis, B. & Terhal, B. M · 2011
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Interplay of topological order and spin glassiness in the toric code under random magnetic fields
Tsomokos, D. I., Osborne, T. J. & Castelnovo, C · 2011
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An improved connected component labeling by recursive label propagation
Kiran, B., Ramakrishnan, K., Kumar, Y. & Anoop, K · 2011
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Bringing order through disorder: Localisation of errors in topological quantum memories
Wootton, J. R. & Pachos, J. K · 2011
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Localization of toric code defects
Stark, C., Imamoglu, A. & Renner, R · 2011
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Quantum memories based on engineered dissipation
Pastawski, F., Clemente, L. & Cirac, J. I · 2011
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Logical operator tradeoff for local quantum codes
Haah, J. & Preskill, J · 2012
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Commuting Pauli Hamiltonians as maps between free modules (2012)
Haah, J · 2012
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Classification of the phases of 1d spin chains with commuting Hamiltonians
Beigi, S · 2012
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Universal topological phase of two-dimensional stabilizer codes
Bombin, H., Duclos-Cianci, G. & Poulin, D · 2012
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A class of highly entangled many-body states that can be efficiently simulated (2012)
Evenbly, G. & Vidal, G · 2012
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Disorder-assisted error correction in Majorana chains
Bravyi, S. & König, R · 2012
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Local topological order inhibits thermal stability in 2D
Landon-Cardinal, O. & Poulin, D · 2013
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