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In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation.
Local stabilizer codes in three dimensions without string logical operators
Jeongwan Haah · 1962
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Quantum-error-correcting codes using qudit graph states
Shiang Looi, Li Yu, Vlad Gheorghiu, and Robert Griffiths · 1979
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A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
Guillaume Duclos-Cianci and Krysta M. Svore · 1980
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Simulating Physics with Computers
Richard P. Feynman · 1982
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A single quantum cannot be cloned
W K Wootters and Wojciech H. Zurek · 1982
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An Algorithm to Compact a VLSI Symbolic Layout with Mixed Constraints
Yuh-Zen Liao and Chak-Kuen Wong · 1983
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An algorithm for optimal two-dimensional compaction of VLSI layouts
Martine Schlag, Yuh-Zen Liao, and Chak-Kuen Wong · 1983
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Two-dimensional layout compaction by simulated annealing
Tsai-Ming Hsieh, Hon Wai Leong, and Chang Liu · 1988
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VLSI cell placement techniques
Khushro Shahookar and Pinaki Mazumder · 1991
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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
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The Theory of Error-Correcting Codes
Florence J. MacWilliams and Neil J.A. Sloane · 1993
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Polynomial Time Algorithms for Discrete Logarithms and Factoring on a Quantum Computer
Peter W. Shor · 1994
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Two-bit gates are universal for quantum computation
David P. DiVincenzo · 1995
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Approximation by Quantum Circuits
Emanuel Knill · 1995
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Mixed State Entanglement and Quantum Error Correction
Charles H. Bennett, David P. DiVincenzo, John A. Smolin, and William K. Wootters · 1996
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Good quantum error-correcting codes exist
A. Robert Calderbank and Peter W. Shor · 1996
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Fault-tolerant error correction with efficient quantum codes
David P. DiVincenzo and Peter W. Shor · 1996
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A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
Daniel Gottesman · 1996
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Pasting Quantum Codes
Daniel Gottesman · 1996
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Concatenated quantum codes
Emanuel Knill and Raymond Laflamme · 1996
Earlier work this paper cites.
Threshold Accuracy for Quantum Computation
Emanuel Knill, Raymond Laflamme, and Wojciech H. Zurek · 1996
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Non-binary unitary error bases and quantum codes
Emanuel Knill · 1996
Earlier work this paper cites.
Quantum Computers and Dissipation
G. Massimo Palma, Kalle-Antti Suominen, and Artur K. Ekert · 1996
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Fault-tolerant quantum computation
Peter W. Shor · 1996
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Active stabilisation, quantum computation and quantum state synthesis
Andrew M. Steane · 1996
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Threshold Estimate for Fault Tolerant Quantum Computing
Christof Zalka · 1996
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Fault Tolerant Quantum Computation with Constant Error
Dorit Aharonov and Michael Ben-Or · 1997
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Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
Daniel Abrams and Seth Lloyd · 1997
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Quantum Error Correction and Orthogonal Geometry
A. Robert Calderbank, Eric M. Rains, Peter W. Shor, and Neil J.A. Sloane · 1997
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Preserving Coherence in Quantum Computation by Pairing Quantum Bits
Lu-Ming Duan and Guang-Can Guo · 1997
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1997
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Quantum computations: algorithms and error correction
Alexei Y. Kitaev · 1997
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Approximate quantum error correction can lead to better codes
Debbie W. Leung, Michael A. Nielsen, Isaac L. Chuang, and Yoshihisa Yamamoto · 1997
Earlier work this paper cites.
Photon-echo technique for reducing the decoherence of a quantum bit
Masashi Ban · 1998
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Quantum codes on a lattice with boundary
Sergey Bravyi and Alexei Y. Kitaev · 1998
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Simulating quantum mechanics on a quantum computer
Bruce M. Boghosian and Washington Taylor · 1998
Earlier work this paper cites.
Experimental Quantum Error Correction
David G. Cory, Mark Price, W. Maas, Emanuel Knill, Raymond Laflamme, Wojciech H. Zurek, Timothy F. Havel, and Shyamal S. Somaroo · 1998
Earlier work this paper cites.
Theory of fault-tolerant quantum computation
Daniel Gottesman · 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.
Handbook of Coding Theory
Vera Pless, Richard A. Brualdi, and W. C. Huffman · 1998
Earlier work this paper cites.
Reliable Quantum Computers
John Preskill · 1998
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Simulating Quantum Systems on a Quantum Computer
Christof Zalka · 1998
Earlier work this paper cites.
PermGroup, 1999, http://wims.unice.fr/wims/en_tool~algebra~permgroup.en.phtml
Xiao Gang · 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.
The Heisenberg Representation of Quantum Computers
Daniel Gottesman · 1999
Earlier work this paper cites.
Concatenating Decoherence-Free Subspaces with Quantum Error Correcting Codes
Daniel A. Lidar, Dave Bacon, and K. Birgitta Whaley · 1999
Earlier work this paper cites.
Experimental realization of a two-bit phase damping quantum code
Debbie W. Leung, Lieven Vandersypen, Xinlan Zhou, Mark Sherwood, Constantino Yannoni, Mark Kubinec, and Isaac L. Chuang · 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 Amplitude Amplification and Estimation
Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp · 2000
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Fast parallel circuits for the quantum Fourier transform
Richard Cleve and John Watrous · 2000
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Fault-Tolerant Quantum Computation with Local Gates
Daniel Gottesman · 2000
Earlier work this paper cites.
Theory of Quantum Error Correction for General Noise
Emanuel Knill, Raymond Laflamme, and Lorenza Viola · 2000
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.
Knots and physics
Louis H. Kauffman · 2001
Earlier work this paper cites.
Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code
Emanuel Knill, Raymond Laflamme, Rudy Martinez, and Camille Negrevergne · 2001
Earlier work this paper cites.
Decoherence-free subspaces for multiple-qubit errors. II. Universal, fault-tolerant quantum computation
Daniel A. Lidar, Dave Bacon, Julia Kempe, and K. Birgitta Whaley · 2001
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Parallel quantum computation and quantum codes
Cristopher Moore and Martin Nilsson · 2001
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Computational model underlying the one-way quantum computer
Robert Raussendorf and Hans Briegel · 2001
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Entanglement required in achieving entanglement-assisted channel capacities
Garry Bowen · 2002
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Experimental Concatenation of Quantum Error Correction with Decoupling
Nicolas Boulant, Marco A. Pravia, Evan M. Fortunato, Timothy F. Havel, and David G. Cory · 2002
Earlier work this paper cites.
Topological quantum memory
Eric Dennis, Alexei Y. Kitaev, Andrew J. Landahl, and John Preskill · 2002
Earlier work this paper cites.
Quantum data hiding
David P. DiVincenzo, Debbie W. Leung, and Barbara M. Terhal · 2002
Earlier work this paper cites.
A modular functor which is universal for quantum computation
Michael H. Freedman, Michael J. Larsen, and Zhenghan Wang · 2002
Earlier work this paper cites.
The Two-Eigenvalue Problem and Density of Jones Representation of Braid Groups
Michael H. Freedman, Michael J. Larsen, and Zhenghan Wang · 2002
Earlier work this paper cites.
Classical and Quantum Computation
Alexei Y. Kitaev, Alexander H. Shen, and Mikhail N. Vyalyi · 2002
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Fast fault-tolerant filtering of quantum codewords
Andrew M. Steane · 2002
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A Simple Proof that Toffoli and Hadamard are Quantum Universal
Dorit Aharonov · 2003
Earlier work this paper cites.
Quantum error correction in globally controlled arrays
Adel Bririd, Simon C. Benjamin, and Alastair Kay · 2003
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How robust is a quantum gate in the presence of noise?
Aram W. Harrow and Michael A. Nielsen · 2003
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Fault-tolerant quantum computation by anyons
Alexei Y. Kitaev · 2003
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Efficient Synthesis of Linear Reversible Circuits
Ketan N. Patel, Igor L. Markov, and John P. Hayes · 2003
Earlier work this paper cites.
Both Toffoli and Controlled-NOT need little help to do universal quantum computation
Yaoyun Shi · 2003
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Overhead and noise threshold of fault-tolerant quantum error correction
Andrew M. Steane · 2003
Earlier work this paper cites.
Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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A new quantum ripple-carry addition circuit
Steven A. Cuccaro, Thomas G. Draper, Samuel A. Kutin, and David P. Moulton · 2004
Earlier work this paper cites.
Realization of quantum error correction
John Chiaverini, D Leibfried, Tobias Schaetz, Murray D Barrett, R B Blakestad, Joseph W. Britton, Wayne M. Itano, Juergen D. Jost, Emanuel Knill, C. E. Langer, Roee Ozeri, and David J. Wineland · 2004
Earlier work this paper cites.
Implementation of Shor’s algorithm on a linear nearest neighbour qubit array
Simon J. Devitt, Austin G. Fowler, and Lloyd C. L. Hollenberg · 2004
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Scalability of Shor’s algorithm with a limited set of rotation gates
Austin G. Fowler and Lloyd C. L. Hollenberg · 2004
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Quantum-error correction on linear-nearest-neighbor qubit arrays
Austin G. Fowler, Charles D. Hill, and Lloyd C. L. Hollenberg · 2004
Earlier work this paper cites.
Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes
Jim Harrington · 2004
Earlier work this paper cites.
Fault-Tolerant Postselected Quantum Computation: Schemes
Emanuel Knill · 2004
Earlier work this paper cites.
Repeat-Until-Success Quantum Computing
Yuan Liang Lim, Almut Beige, and Leong Chuan Kwek · 2004
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Improved ancilla preparation scheme increases fault-tolerant threshold
Ben W. Reichardt · 2004
Earlier work this paper cites.
Universal quantum computation with ideal Clifford gates and noisy ancillas
Sergey Bravyi and Alexei Y. Kitaev · 2005
Earlier work this paper cites.
Experimental Implementation of a Concatenated Quantum Error-Correcting Code
Nicolas Boulant, Lorenza Viola, Evan Fortunato, and David G. Cory · 2005
Earlier work this paper cites.
Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
Sankar Das Sarma, Michael H. Freedman, and Chetan Nayak · 2005
Cited alongside, same era.
The Solovay-Kitaev algorithm
Christopher M. Dawson and Michael A. Nielsen · 2005
Cited alongside, same era.
Error Correcting the Control Unit in Global Control Schemes
Alastair Kay · 2005
Cited alongside, same era.
Quantum Computing with Very Noisy Devices
Emanuel Knill · 2005
Cited alongside, same era.
A quantum logic array microarchitecture: Scalable quantum data movement and computation
Tzvetan Metodi, Darshan Thaker, Andrew W. Cross, Fred Chong, and Isaac L. Chuang · 2005
Cited alongside, same era.
Demonstration of quantum error correction using linear optics
T. Pittman, B. Jacobs, and J. D. Franson · 2005
Cited alongside, same era.
Experimental repetitive quantum error correction
Philipp Schindler, Julio T. Barreiro, Thomas Monz, Volckmar Nebendahl, Daniel Nigg, Michael Chwalla, Markus Hennrich, and Rainer Blatt · 2011
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Long-term performance of the SwissQuantum quantum key distribution network in a field environment
D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden · 2011
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The Role of Correlated Noise in Quantum Computing
Daan Staudt · 2011
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Experimental magic state distillation for fault-tolerant quantum computing
Alexandre M. Souza, Jingfu Zhang, Colm A. Ryan, and Raymond Laflamme · 2011
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Quantum Universality from Magic States Distillation Applied to CSS Codes
Ben W. Reichardt · 2005
Cited alongside, same era.
Local fault-tolerant quantum computation
Krysta M. Svore, Barbara M. Terhal, and David P. DiVincenzo · 2005
Cited alongside, same era.
Fault-tolerant quantum computation for local non-Markovian noise
Barbara M. Terhal and Guido Burkard · 2005
Cited alongside, same era.
Classical simulatability, entanglement breaking, and quantum computation thresholds
Shashank Virmani, Susana F. Huelga, and Martin B. Plenio · 2005
Cited alongside, same era.
Quantum accuracy threshold for concatenated distance-3 codes
Panos Aliferis, Daniel Gottesman, and John Preskill · 2006
Cited alongside, same era.
Fault-Tolerant Quantum Computation with Long-Range Correlated Noise
Dorit Aharonov, Alexei Y. Kitaev, and John Preskill · 2006
Cited alongside, same era.
David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg · 2011
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Transversality versus universality for additive quantum codes
Bei Zeng, Andrew W. Cross, and Isaac L. Chuang · 2011
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Experimental quantum error correction with high fidelity
Jingfu Zhang, Dorian Gangloff, Osama Moussa, and Raymond Laflamme · 2011
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A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
Matthew Amy, Dmitri Maslov, Michele Mosca, and Martin Roetteler · 2012
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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Classification of topologically protected gates for local stabilizer codes
Sergey Bravyi and Robert König · 2012
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Koichi Betsumiya and Akihiro Munemasa · 2012
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Fault-tolerant quantum computation with asymmetric Bacon-Shor codes
Peter Brooks and John Preskill · 2012
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A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits
Alex Bocharov and Krysta M. Svore · 2012
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Magic state distillation in all prime dimensions using quantum Reed-Muller codes
Earl T. Campbell, Hussain Anwar, and Dan E. Browne · 2012
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Jerry M. Chow, Jay M. Gambetta, Antonio D. Corcoles, Seth T. Merkel, John A. Smolin, Chad Rigetti, S. Poletto, George A. Keefe, Mary B. Rothwell, John R. Rozen, Mark B. Ketchen, and Matthias Steffen · 2012
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A bridge to lower overhead quantum computation
Austin G. Fowler and Simon J. Devitt · 2012
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A primer on surface codes: Developing a machine language for a quantum computer
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
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Low-overhead surface code logical H
Austin G. Fowler · 2012
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Proof of finite surface code threshold for matching
Austin G. Fowler · 2012
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Time-optimal quantum computation
Austin G. Fowler · 2012
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Implementation of a Toffoli gate with superconducting circuits
Arkady Fedorov, Lars Steffen, Matthias Baur, Marcus P. da Silva, and Andreas Wallraff · 2012
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Towards practical classical processing for the surface code
Austin G. Fowler, Adam C. Whiteside, and Lloyd C. L. Hollenberg · 2012
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Austin G. Fowler, Adam C. Whiteside, Angus L. McInnes, and Alimohammad Rabbani · 2012
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Surface code with decoherence: An analysis of three superconducting architectures
Joydip Ghosh, Austin G. Fowler, and MR Geller · 2012
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Exact synthesis of multi-qubit Clifford+T circuits
Brett Giles and Peter Selinger · 2012
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Surface code quantum computing by lattice surgery
Clare Horsman, Austin G. Fowler, Simon J. Devitt, and Rodney Van Meter · 2012
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Multilevel distillation of magic states for quantum computing
Cody Jones · 2012
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Layered Architecture for Quantum Computing
Cody Jones, Rodney Van Meter, Austin G. Fowler, Peter L. McMahon, Jungsang Kim, Thaddeus D. Ladd, and Yoshihisa Yamamoto · 2012
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Simulating chemistry efficiently on fault-tolerant quantum computers
Cody Jones, James D. Whitfield, Peter L. McMahon, Man-Hong Yung, Rodney Van Meter, Alán Aspuru-Guzik, and Yoshihisa Yamamoto · 2012
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The robustness of magic state distillation against errors in Clifford gates
Tomas Jochym-O’Connor, Yafei Yu, Bassam Helou, and Raymond Laflamme · 2012
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3D local qupit quantum code without string logical operator
Isaac H. Kim · 2012
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Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2012
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Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates
Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2012
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Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits
Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2012
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Interacting Fibonacci anyons in a Rydberg gas
Igor Lesanovsky and Hosho Katsura · 2012
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Checking the error correction strength of arbitrary surface code logical gates
Thomas J. Milburn and Austin G. Fowler · 2012
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3-d quantum stabilizer codes with a power law energy barrier
Kamil Michnicki · 2012
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Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code
Adam Paetznick and Ben W. Reichardt · 2012
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Realization of three-qubit quantum error correction with superconducting circuits
Matthew D. Reed, Leonardo DiCarlo, Simon E. Nigg, Luyan Sun, Luigi Frunzio, Steven M. Girvin, and Robert J. Schoelkopf · 2012
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Efficient Clifford+T approximation of single-qubit operators
Peter Selinger · 2012
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Experimental Implementation of a Codeword Stabilized Quantum Code
Jingfu Zhang, Markus Grassl, Bei Zeng, and Raymond Laflamme · 2012
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Jingfu Zhang, Raymond Laflamme, and Dieter Suter · 2012
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Algorithms for the Optimization of Quantum Circuits
Matthew Amy · 2013
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Self-correcting quantum computers
Hector Bombin, Ravindra W. Chhajlany, Michał Horodecki, and Miguel-Angel Martin-Delgado · 2013
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Efficient Decomposition of Single-Qubit Gates into V Basis Circuits
Alex Bocharov, Yuri Gurevich, and Krysta M. Svore · 2013
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Quantum error correction with biased noise
Peter Brooks · 2013
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In preparation
Andrew M. Childs and Robin Kothari · 2013
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Global Quantum Circuit Optimization
Raphael Dias da Silva, Einar Pius, and Elham Kashefi · 2013
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Distilling one-qubit magic states into Toffoli states
Bryan Eastin · 2013
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Surface code implementation of block code state distillation
Austin G. Fowler, Simon J. Devitt, and Cody Jones · 2013
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Coping with qubit leakage in topological codes
Austin G. Fowler · 2013
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Minimum weight perfect matching in O(1) parallel time
Austin G. Fowler · 2013
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Optimal complexity correction of correlated errors in the surface code
Austin G. Fowler · 2013
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Joydip Ghosh, Austin G. Fowler, John M. Martinis, and Michael R. Geller · 2013
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High-fidelity CZ gate for resonator-based superconducting quantum computers
Joydip Ghosh, Andrei Galiautdinov, and Zhongyuan Zhou · 2013
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David Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo · 2013
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Quantum 3-SAT is QMA1-complete
David Gosset and Daniel Nagaj · 2013
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What is the Overhead Required for Fault-Tolerant Quantum Computation?
Daniel Gottesman · 2013
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An 8-bit carry look-ahead adder with 150 ps latency and sub-microwatt power dissipation at 10 GHz
Anna Y. Herr, Quentin P. Herr, Oliver T. Oberg, Ofer Naaman, John X. Przybysz, Pavel Borodulin, and Steven B. Shauck · 2013
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Energy-Efficient Superconducting Computing—Power Budgets and Requirements
D. Scott Holmes, Andrew L. Ripple, and Marc A. Manheimer · 2013
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Using concatenated quantum codes for universal fault-tolerant quantum gates
Tomas Jochym-O’Connor and Raymond Laflamme · 2013
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Composite Toffoli gate with two-round error detection
Cody Jones · 2013
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Distillation protocols for Fourier states in quantum computing
Cody Jones · 2013
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Logic synthesis for fault-tolerant quantum computers
Cody Jones · 2013
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Low-overhead constructions for the fault-tolerant Toffoli gate
Cody Jones · 2013
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Synthesis of unitaries with Clifford+T circuits
Vadym Kliuchnikov · 2013
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Andrew J. Landahl and Chris Cesare · 2013
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Performance and Error Analysis of Knill’s Postselection Scheme in a Two-Dimensional Architecture
Ching-Yi Lai, Gerardo Paz, Martin Suchara, and Todd A. Brun · 2013
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Magic-state distillation with the four-qubit code
Adam M. Meier, Bryan Eastin, and Emanuel Knill · 2013
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Modeling quantum noise for efficient testing of fault-tolerant circuits
Easwar Magesan, Daniel Puzzuoli, Christopher E. Granade, and David G. Cory · 2013
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Quantum circuit optimization by topological compaction in the surface code
Adam Paetznick and Austin G. Fowler · 2013
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Universal fault-tolerant quantum computation with only transversal gates and error correction
Adam Paetznick and Ben W. Reichardt · 2013
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Sufficient condition on noise correlations for scalable quantum computing
John Preskill · 2013
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Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries
Adam Paetznick and Krysta M. Svore · 2013
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Optimally combining dynamical decoupling and quantum error correction
Gerardo A. Paz-Silva and Daniel A. Lidar · 2013
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Quantum circuits of T-depth one
Peter Selinger · 2013
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Topological quantum computation–from basic concepts to first experiments
Ady Stern and Netanel H Lindner · 2013
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High-threshold topological quantum error correction against biased noise
Ashley M. Stephens, William J. Munro, and Kae Nemoto · 2013
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Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures
Alireza Shafaei, Mehdi Saeedi, and Massoud Pedram · 2013
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Implementation of energy efficient single flux quantum digital circuits with sub-aJ/bit operation
Mark H. Volkmann, Anubhav Sahu, Coenrad J. Fourie, and Oleg A. Mukhanov · 2013
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Private communication
Dave Wecker, Bela Bauer, Bryan Clark, and Matthias Troyer · 2013
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Efficient Quantum Circuits for Diagonal Unitaries Without Ancillas
Jonathan Welch, Daniel Greenbaum, Sarah Mostame, and Alán Aspuru-Guzik · 2013
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Floating point representations in quantum circuit synthesis
Nathan Wiebe and Vadym Kliuchnikov · 2013
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Quantum Logic between Remote Quantum Registers
Norman Y. Yao, Zhe-Xuan Gong, Chris R. Laumann, Steven D. Bennett, L. M. Duan, Mikhail D. Lukin, Liang Jiang, and Alexey V. Gorshkov · 2013
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Topological one-way quantum computation on verified logical cluster states
Keisuke Fujii and Katsuji Yamamoto · 2048
Closest in time.
Ancilla Driven Quantum Computation with arbitrary entangling strength
Kerem Halil Shah and Daniel Kuan Li Oi · 2066
Closest in time.