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This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes.
About the pauli exclusion principle
P Jordan and Eugene P Wigner · 1928
Earlier work this paper cites.
Can quantum-mechanical description of physical reality be considered complete?
Albert Einstein, Boris Podolsky, and Nathan Rosen · 1935
Earlier work this paper cites.
Statistics of the two-dimensional ferromagnet. part i
Hendrik A Kramers and Gregory H Wannier · 1941
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The statistics of dimers on a lattice: I. the number of dimer arrangements on a quadratic lattice
Pieter W Kasteleyn · 1961
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Paths, trees, and flowers
Jack Edmonds · 1965
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Relations between the’percolation’and’colouring’problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the’percolation’problem
Harold NV Temperley and Elliott H Lieb · 1971
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The theory of error correcting codes
Florence Jessie MacWilliams and Neil James Alexander Sloane · 1977
Earlier work this paper cites.
Conjecture on the exact transition point of the random ising ferromagnet
Hidetoshi Nishimori · 1979
Earlier work this paper cites.
Internal energy, specific heat and correlation function of the bond-random ising model
Hidetoshi Nishimori · 1981
Earlier work this paper cites.
On the computational complexity of ising spin glass models
Francisco Barahona · 1982
Earlier work this paper cites.
Simulating physics with computers
Richard P Feynman · 1982
Earlier work this paper cites.
Reversibility and stability of information processing systems
Wojciech H Zurek · 1984
Earlier work this paper cites.
Quantum theory, the church-turing principle and the universal quantum computer
David Deutsch · 1985
Earlier work this paper cites.
Going beyond bell’s theorem
Daniel M Greenberger, Michael A Horne, and Anton Zeilinger · 1989
Earlier work this paper cites.
Quantum field theory and the jones polynomial
Edward Witten · 1989
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Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels
Charles H Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K Wootters · 1993
Earlier work this paper cites.
Quantum optical master equations: The use of damping bases
Hans-Jürgen Briegel and Berthold-Georg Englert · 1993
Earlier work this paper cites.
Quantum complexity theory
Ethan Bernstein and Umesh Vazirani · 1993
Earlier work this paper cites.
Experimental realization of any discrete unitary operator
Michael Reck, Anton Zeilinger, Herbert J Bernstein, and Philip Bertani · 1994
Earlier work this paper cites.
Algorithms for quantum computation: discrete logarithms and factoring
P. W. Shor · 1994
Earlier work this paper cites.
Elementary gates for quantum computation
Adriano Barenco, Charles H Bennett, Richard Cleve, David P DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A Smolin, and Harald Weinfurter · 1995
Earlier work this paper cites.
Two-bit gates are universal for quantum computation
David P DiVincenzo · 1995
Earlier work this paper cites.
Perturbation theory for linear operators
Tosio Kato · 1995
Earlier work this paper cites.
Quantum measurements and the abelian stabilizer problem
A Yu Kitaev · 1995
Earlier work this paper cites.
Quantum measurements and the abelian stabilizer problem
A Yu Kitaev · 1995
Earlier work this paper cites.
Scheme for reducing decoherence in quantum computer memory
Peter W. Shor · 1995
Earlier work this paper cites.
Mixed-state entanglement and quantum error correction
Charles H Bennett, David P DiVincenzo, John A Smolin, and William K Wootters · 1996
Earlier work this paper cites.
Good quantum error-correcting codes exist
A Robert Calderbank and Peter W Shor · 1996
Earlier work this paper cites.
Fault-tolerant error correction with efficient quantum codes
David P. DiVincenzo and Peter W. Shor · 1996
Earlier work this paper cites.
A fast quantum mechanical algorithm for database search
Lov K Grover · 1996
Earlier work this paper cites.
Perfect quantum error correcting code
Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, and Wojciech Hubert Zurek · 1996
Earlier work this paper cites.
Error correcting codes in quantum theory
Andrew M Steane · 1996
Earlier work this paper cites.
Error prevention scheme with four particles
Lev Vaidman, Lior Goldenberg, and Stephen Wiesner · 1996
Earlier work this paper cites.
Fault tolerant quantum computation with constant error
Dorit Aharonov and Michael Ben-Or · 1997
Earlier work this paper cites.
Preserving coherence in quantum computation by pairing quantum bits
Lu-Ming Duan and Guang-Can Guo · 1997
Earlier work this paper cites.
Stabilizer codes and quantum error correction
D Gottesman · 1997
Earlier work this paper cites.
Quantum computations: algorithms and error correction
A Yu Kitaev · 1997
Earlier work this paper cites.
Finite-size scaling analysis of exact ground states for ± \pm j spin glass models in two dimensions
Naoki Kawashima and Heiko Rieger · 1997
Earlier work this paper cites.
An introduction to knot theory
WB Raymond Lickorish · 1997
Earlier work this paper cites.
Conditional generation of error syndromes in fault-tolerant error correction
MB Plenio, V Vedral, and PL Knight · 1997
Earlier work this paper cites.
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Peter W Shor · 1997
Earlier work this paper cites.
Active stabilization, quantum computation, and quantum state synthesis
Andrew M Steane · 1997
Earlier work this paper cites.
Noiseless quantum codes
Paolo Zanardi and Mario Rasetti · 1997
Earlier work this paper cites.
Prevention of dissipation with two particles
Lu-Ming Duan and Guang-Can Guo · 1998
Earlier work this paper cites.
The heisenberg representation of quantum computers
Daniel Gottesman · 1998
Earlier work this paper cites.
The heisenberg representation of quantum computers
Daniel Gottesman · 1998
Earlier work this paper cites.
Power of one bit of quantum information
E. Knill and R. Laflamme · 1998
Earlier work this paper cites.
Resilient quantum computation
Emanuel Knill, Raymond Laflamme, and Wojciech H Zurek · 1998
Earlier work this paper cites.
Resilient quantum computation: error models and thresholds
Emanuel Knill, Raymond Laflamme, and Wojciech H Zurek · 1998
Earlier work this paper cites.
Decoherence-free subspaces for quantum computation
D. A. Lidar, I. L. Chuang, and K. B. Whaley · 1998
Earlier work this paper cites.
Decoherence-free subspaces for quantum computation
Daniel A Lidar, Isaac L Chuang, and K Birgitta Whaley · 1998
Earlier work this paper cites.
Dynamical suppression of decoherence in two-state quantum systems
Lorenza Viola and Seth Lloyd · 1998
Earlier work this paper cites.
Computing minimum-weight perfect matchings
William Cook and Andre Rohe · 1999
Earlier work this paper cites.
Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
Daniel Gottesman and Isaac L Chuang · 1999
Earlier work this paper cites.
Domain-wall free energy of spin-glass models: Numerical method and boundary conditions
Koji Hukushima · 1999
Earlier work this paper cites.
Obituary: Rolf landauer (1927-99)
Seth Lloyd · 1999
Earlier work this paper cites.
Coherent control of macroscopic quantum states in a single-cooper-pair box
Yu Nakamura, Yu A Pashkin, and JS Tsai · 1999
Earlier work this paper cites.
Universality, frustration, and conformal invariance in two-dimensional random ising magnets
FDA Aarao Reis, SLA De Queiroz, and Raimundo R Dos Santos · 1999
Earlier work this paper cites.
Efficient fault-tolerant quantum computing
Andrew M Steane · 1999
Earlier work this paper cites.
Dynamical decoupling of open quantum systems
Lorenza Viola, Emanuel Knill, and Seth Lloyd · 1999
Earlier work this paper cites.
Dynamical decoupling of open quantum systems
Lorenza Viola, Emanuel Knill, and Seth Lloyd · 1999
Earlier work this paper cites.
Quantum computation and quantum information
Michael A Nielsen and Isaac L Chuang · 2000
Earlier work this paper cites.
Methodology for quantum logic gate construction
Xinlan Zhou, Debbie W Leung, and Isaac L Chuang · 2000
Earlier work this paper cites.
Persistent entanglement in arrays of interacting particles
Hans J Briegel and Robert Raussendorf · 2001
Earlier work this paper cites.
Universality class of the nishimori point in the 2d ± \pm j random-bond ising model
Andreas Honecker, Marco Picco, and Pierre Pujol · 2001
Earlier work this paper cites.
Unpaired majorana fermions in quantum wires
A Yu Kitaev · 2001
Earlier work this paper cites.
Statistical physics of spin glasses and information processing
Hidetoshi Nishimori · 2001
Earlier work this paper cites.
A one-way quantum computer
Robert Raussendorf and Hans J Briegel · 2001
Earlier work this paper cites.
Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
Earlier work this paper cites.
Two-dimensional random-bond ising model, free fermions, and the network model
F Merz and JT Chalker · 2002
Earlier work this paper cites.
Duality and multicritical point of two-dimensional spin glasses
Hidetoshi Nishimori and Koji Nemoto · 2002
Cited alongside, same era.
The theory of open quantum systems
Francesco Petruccione and Heinz-Peter Breuer · 2002
Cited alongside, same era.
Coherent quantum dynamics of a superconducting flux qubit
I Chiorescu, Y Nakamura, CJP Ma Harmans, and JE Mooij · 2003
Cited alongside, same era.
Multiparticle entanglement purification for graph states
Wolfgang Dür, Hans Aschauer, and H-J Briegel · 2003
Cited alongside, same era.
Topological quantum computation
Michael Freedman, Alexei Kitaev, Michael Larsen, and Zhenghan Wang · 2003
Cited alongside, same era.
Fault-tolerant quantum computation by anyons
A Yu Kitaev · 2003
Cited alongside, same era.
Thresholds for topological codes in the presence of loss
Thomas M Stace, Sean D Barrett, and Andrew C Doherty · 2009
Later among the works it cites.
Topological order with a twist: Ising anyons from an abelian model
Hctor Bombin · 2010
Later among the works it cites.
Fast decoders for topological quantum codes
Guillaume Duclos-Cianci and David Poulin · 2010
Later among the works it cites.
A renormalization group decoding algorithm for topological quantum codes
Guillaume Duclos-Cianci and David Poulin · 2010
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Fault-tolerant topological one-way quantum computation with probabilistic two-qubit gates
Keisuke Fujii and Yuuki Tokunaga · 2010
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Cluster-based architecture for fault-tolerant quantum computation
Keisuke Fujii and Katsuji Yamamoto · 2010
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Measurement-based quantum computation with cluster states
R Raussendorf · 2003
Cited alongside, same era.
Measurement-based quantum computation on cluster states
Robert Raussendorf, Daniel E Browne, and Hans J Briegel · 2003
Cited alongside, same era.
Overhead and noise threshold of fault-tolerant quantum error correction
Andrew M Steane · 2003
Cited alongside, same era.
Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
Chenyang Wang, Jim Harrington, and John Preskill · 2003
Cited alongside, same era.
Demonstration of conditional gate operation using superconducting charge qubits
Tsuyoshi Yamamoto, Yu A Pashkin, Oleg Astafiev, Yasunobu Nakamura, and Jaw-Shen Tsai · 2003
Cited alongside, same era.
Deterministic linear optics quantum computation with single photon qubits
Nadav Yoran and Benni Reznik · 2003
Cited alongside, same era.
Topological one-way quantum computation on verified logical cluster states
Keisuke Fujii and Katsuji Yamamoto · 2010
Later among the works it cites.
Fault tolerant quantum computation with nondeterministic gates
Ying Li, Sean D Barrett, Thomas M Stace, and Simon C Benjamin · 2010
Later among the works it cites.
Probabilistic growth of large entangled states with low error accumulation
Yuichiro Matsuzaki, Simon C Benjamin, and Joseph Fitzsimons · 2010
Later among the works it cites.
Entanglement spectrum of a topological phase in one dimension
Frank Pollmann, Ari M Turner, Erez Berg, and Masaki Oshikawa · 2010
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Error correction and degeneracy in surface codes suffering loss
Thomas M Stace and Sean D Barrett · 2010
Later among the works it cites.
Distributed quantum computation architecture using semiconductor nanophotonics
Rodney Van Meter, Thaddeus D Ladd, Austin G Fowler, and Yoshihisa Yamamoto · 2010
Later among the works it cites.
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
Michael J Bremner, Richard Jozsa, and Dan J Shepherd · 2011
Later among the works it cites.
Clifford gates by code deformation
H Bombin · 2011
Later among the works it cites.
Quantum algorithms for classical lattice models
G De las Cuevas, W Dür, M Van den Nest, and MA Martin-Delgado · 2011
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Np-hardness of decoding quantum error-correction codes
Min-Hsiu Hsieh and François Le Gall · 2011
Later among the works it cites.
Thermal states as universal resources for quantum computation with always-on interactions
Ying Li, Daniel E Browne, Leong Chuan Kwek, Robert Raussendorf, and Tzu-Chieh Wei · 2011
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Surface code quantum computing with error rates over 1%
David S Wang, Austin G Fowler, and Lloyd CL Hollenberg · 2011
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Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
Beni Yoshida · 2011
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Feasibility of self-correcting quantum memory and thermal stability of topological order
Beni Yoshida · 2011
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Strong resilience of topological codes to depolarization
H Bombin, Ruben S Andrist, Masayuki Ohzeki, Helmut G Katzgraber, and MA Martin-Delgado · 2012
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Universal topological phase of two-dimensional stabilizer codes
Héctor Bombín, Guillaume Duclos-Cianci, and David Poulin · 2012
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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Universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
Jerry M Chow, Jay M Gambetta, AD Córcoles, Seth T Merkel, John A Smolin, Chad Rigetti, S Poletto, George A Keefe, Mary B Rothwell, JR Rozen, et al · 2012
Later among the works it cites.
Topologically protected measurement-based quantum computation on the thermal state of a nearest-neighbor two-body hamiltonian with spin-3/2 particles
Keisuke Fujii and Tomoyuki Morimae · 2012
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Surface codes: Towards practical large-scale quantum computation
Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland · 2012
Later among the works it cites.
Error and loss tolerances of surface codes with general lattice structures
Keisuke Fujii and Yuuki Tokunaga · 2012
Later among the works it cites.
Towards practical classical processing for the surface code
Austin G Fowler, Adam C Whiteside, and Lloyd CL Hollenberg · 2012
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A distributed architecture for scalable quantum computation with realistically noisy devices
Keisuke Fujii, Takashi Yamamoto, Masato Koashi, and Nobuyuki Imoto · 2012
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Surface code with decoherence: An analysis of three superconducting architectures
Joydip Ghosh, Austin G Fowler, and Michael R Geller · 2012
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Surface code quantum computing by lattice surgery
Clare Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter · 2012
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Layered architecture for quantum computing
N Cody Jones, Rodney Van Meter, Austin G Fowler, Peter L McMahon, Jungsang Kim, Thaddeus D Ladd, and Yoshihisa Yamamoto · 2012
Later among the works it cites.
On the hardness of decoding quantum stabilizer codes under the depolarizing channel
Kao-Yueh Kuo and Chung-Chin Lu · 2012
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High threshold distributed quantum computing with three-qubit nodes
Ying Li and Simon C Benjamin · 2012
Later among the works it cites.
Magic-state distillation with the four-qubit code
Adam M Meier, Bryan Eastin, and Emanuel Knill · 2012
Later among the works it cites.
Blind topological measurement-based quantum computation
Tomoyuki Morimae and Keisuke Fujii · 2012
Later among the works it cites.
Duality analysis on random planar lattices
Masayuki Ohzeki and Keisuke Fujii · 2012
Later among the works it cites.
Error threshold estimates for surface code with loss of qubits
Masayuki Ohzeki · 2012
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Introduction to topological quantum computation
Jiannis K Pachos · 2012
Later among the works it cites.
Incoherent dynamics in the toric code subject to disorder
Beat Röthlisberger, James R Wootton, Robert M Heath, Jiannis K Pachos, and Daniel Loss · 2012
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Lifetime of topological quantum memories in thermal environment
Abbas Al-Shimary, James R Wootton, and Jiannis K Pachos · 2013
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Distilling one-qubit magic states into toffoli states
Bryan Eastin · 2013
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Measurement-based quantum computation on symmetry breaking thermal states
Keisuke Fujii, Yoshifumi Nakata, Masayuki Ohzeki, and Mio Murao · 2013
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Hardness of decoding quantum stabilizer codes
Pavithran Iyer and David Poulin · 2013
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Low-overhead constructions for the fault-tolerant toffoli gate
Cody Jones · 2013
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Multilevel distillation of magic states for quantum computing
Cody Jones · 2013
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Blind quantum computation protocol in which alice only makes measurements
Tomoyuki Morimae and Keisuke Fujii · 2013
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Topological quantum computing with a very noisy network and local error rates approaching one percent
Naomi H Nickerson, Ying Li, and Simon C Benjamin · 2013
Later among the works it cites.
Spin glass: A bridge between quantum computing and statistical mechanics
Masayuki Ohzeki · 2013
Later among the works it cites.
Enhanced thermal stability of the toric code through coupling to a bosonic bath
Fabio L Pedrocchi, Adrian Hutter, James R Wootton, and Daniel Loss · 2013
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Superconducting quantum circuits at the surface code threshold for fault tolerance
R Barends, J Kelly, A Megrant, A Veitia, D Sank, E Jeffrey, TC White, J Mutus, AG Fowler, B Campbell, et al · 2014
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Superconducting quantum circuits at the surface code threshold for fault tolerance
R Barends, J Kelly, A Megrant, A Veitia, D Sank, E Jeffrey, TC White, J Mutus, AG Fowler, B Campbell, et al · 2014
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Implementing a strand of a scalable fault-tolerant quantum computing fabric
Jerry M Chow, Jay M Gambetta, Easwar Magesan, Srikanth J Srinivasan, Andrew W Cross, David W Abraham, Nicholas A Masluk, BR Johnson, Colm A Ryan, and M Steffen · 2014
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Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
AD Córcoles, Easwar Magesan, Srikanth J Srinivasan, Andrew W Cross, M Steffen, Jay M Gambetta, and Jerry M Chow · 2014
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Decoding color codes by projection onto surface codes
Nicolas Delfosse · 2014
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Measurement-free topological protection using dissipative feedback
Keisuke Fujii, Makoto Negoro, Nobuyuki Imoto, and Masahiro Kitagawa · 2014
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Computational quantum-classical boundary of commuting quantum circuits
Keisuke Fujii and Shuhei Tamate · 2014
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Quantum computer quest
Elizabeth Gibney · 2014
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Cellular-automaton decoders for topological quantum memories
M Herold, ET Campbell, J Eisert, and MJ Kastoryano · 2014
Later among the works it cites.
Low depth quantum circuits for ising models
S Iblisdir, M Cirio, O Boada, and GK Brennen · 2014
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Implications of ignorance for quantum-error-correction thresholds
Alastair Kay · 2014
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State preservation by repetitive error detection in a superconducting quantum circuit
J. Kelly, R. Barends, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, et al · 2014
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Eliot Kapit, John T Chalker, and Steven H Simon · 2014
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Hardness of classically simulating the one-clean-qubit model
Tomoyuki Morimae, Keisuke Fujii, and Joseph F. Fitzsimons · 2014
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Quantum algorithm for an additive approximation of ising partition functions
Akira Matsuo, Keisuke Fujii, and Nobuyuki Imoto · 2014
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Tomoyuki Morimae, Harumichi Nishimura, Keisuke Fujii, and Shuhei Tamate · 2014
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Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects
C Monroe, R Raussendorf, A Ruthven, KR Brown, P Maunz, L-M Duan, and J Kim · 2014
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A silicon-based surface code quantum computer
Joe O’Gorman, Naomi H Nickerson, Philip Ross, John JL Morton, and Simon C Benjamin · 2014
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Perturbative instability of quantum memory based on effective long-range interactions
Olivier Landon-Cardinal, Beni Yoshida, David Poulin, and John Preskill · 2015
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