Built on

Peter W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52
1995
Earlier work this paper cites.
E Knill, R Laflamme, and W Zurek, “Threshold accuracy for quantum computation,” quant-ph/9610011 (1996), quant-ph/9610011
1996
Earlier work this paper cites.
P. W. Shor, “Fault-tolerant quantum computation,” in Proc. 37th IEEE Symp. Found. Comp. Sci. (FOCS) (1996) p. 56, quant-ph/9605011
1996
Earlier work this paper cites.
Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, and Wojciech Hubert Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77
1996
Earlier work this paper cites.
A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77
1996
Earlier work this paper cites.
D. Aharonov and M. Ben-Or, “Fault-tolerant quantum computation with constant error rate,” in 29th ACM Symp. on Theory of Computing (STOC) (New York, 1997) pp. 176–188
1997
Earlier work this paper cites.
A. Yu. Kitaev, “Quantum error correction with imperfect gates,” in Quantum Communication, Computing, and Measurement (Springer US, 1997) pp. 181–188
1997
Earlier work this paper cites.
A Robert Calderbank, Eric M Rains, PM Shor, and Neil JA Sloane, “Quantum error correction via codes over GF(4),” IEEE Transactions on Information Theory 44
1998
Earlier work this paper cites.
S. B. Bravyi and A. Yu. Kitaev, “Quantum codes on a lattice with boundary,” (1998) , quant-ph/9811052
1998
Earlier work this paper cites.
Eric M. Rains, “Quantum codes of minimum distance two,” IEEE Transactions on Information theory 45
1999
Earlier work this paper cites.
Michael N. Nielsen and Isaac L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)
2000
Earlier work this paper cites.
A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi, Classical and Quantum Computation (American Mathematical Society, 2002)
2002
Earlier work this paper cites.
Benjamin Rahn, Andrew C. Doherty, and Hideo Mabuchi, “Exact Performance of Concatenated Quantum Codes,” Phys. Rev. A 66
2002
Earlier work this paper cites.
Panos Aliferis, Daniel Gottesman, and John Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quant. Inf. Comput. 6
2006
Earlier work this paper cites.
J. Fern, J. Kempe, S. N. Simic, and S. Sastry, “Generalized performance of concatenated quantum codes — a dynamical systems approach,” IEEE Transactions on Automatic Control 51
2006
Earlier work this paper cites.
David Poulin, “Optimal and efficient decoding of concatenated quantum block codes,” Phys. Rev. A 74
2006
Earlier work this paper cites.

Similar

P. Aliferis and A. W. Cross, “Subsystem fault tolerance with the Bacon-Shor code,” Phys. Rev. Lett. 98
2007
Cited alongside, same era.
E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Randomized benchmarking of quantum gates,” Phys. Rev. A 77
Original
2008
Cited alongside, same era.
Andrew S. Fletcher, Peter W. Shor, and Moe Z. Win, “Structured near-optimal channel-adapted quantum error correction,” Phys. Rev. A 77
Original
2008
Cited alongside, same era.
David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg, “Surface code quantum computing with error rates over 1%,” Phys. Rev. A 83
Original
2011
Cited alongside, same era.
Bei Zeng, Andrew Cross, and Isaac L Chuang, “Transversality versus universality for additive quantum codes,” IEEE Transactions on Information Theory 57

Then

Mauricio Gutiérrez and Kenneth R. Brown, “Comparison of a quantum error-correction threshold for exact and approximate errors,” Phys. Rev. A 91
Original
2015
Later among the works it cites.
Mauricio Gutiérrez, Conor Smith, Livia Lulushi, Smitha Janardan, and Kenneth R. Brown, “Errors and pseudo-thresholds for incoherent and coherent noise,” Phys. Rev. A 94
Original
2016
Later among the works it cites.
Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz, “Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography,” Nature Communications 8
Original
2016
Later among the works it cites.
Richard Kueng, David M. Long, Andrew C. Doherty, and Steven T. Flammia, “Comparing experiments to the fault-tolerance threshold,” Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.

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2018

Performance of quantum error correction with coherent errors

Huang, Eric, Doherty, Andrew C., Flammia, Steven

Understand

We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise.

For a wide range of codes we analytically compute the effective logical channel that results when the error correction steps are performed noiselessly.
Our examples include the entire family of repetition codes, the 5-qubit, Steane, Shor, and surface codes.
When errors are measured in terms of the diamond norm, we find that the error correction is typically much more effective for unitary errors than for dephasing.

Built on

Peter W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52
1995
Earlier work this paper cites.
E Knill, R Laflamme, and W Zurek, “Threshold accuracy for quantum computation,” quant-ph/9610011 (1996), quant-ph/9610011
1996
Earlier work this paper cites.
P. W. Shor, “Fault-tolerant quantum computation,” in Proc. 37th IEEE Symp. Found. Comp. Sci. (FOCS) (1996) p. 56, quant-ph/9605011
1996
Earlier work this paper cites.
Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, and Wojciech Hubert Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77
1996
Earlier work this paper cites.
A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77
1996
Earlier work this paper cites.
D. Aharonov and M. Ben-Or, “Fault-tolerant quantum computation with constant error rate,” in 29th ACM Symp. on Theory of Computing (STOC) (New York, 1997) pp. 176–188
1997
Earlier work this paper cites.
A. Yu. Kitaev, “Quantum error correction with imperfect gates,” in Quantum Communication, Computing, and Measurement (Springer US, 1997) pp. 181–188
1997
Earlier work this paper cites.
A Robert Calderbank, Eric M Rains, PM Shor, and Neil JA Sloane, “Quantum error correction via codes over GF(4),” IEEE Transactions on Information Theory 44
1998
Earlier work this paper cites.
S. B. Bravyi and A. Yu. Kitaev, “Quantum codes on a lattice with boundary,” (1998) , quant-ph/9811052
1998
Earlier work this paper cites.
Eric M. Rains, “Quantum codes of minimum distance two,” IEEE Transactions on Information theory 45
1999
Earlier work this paper cites.
Michael N. Nielsen and Isaac L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)
2000
Earlier work this paper cites.
A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi, Classical and Quantum Computation (American Mathematical Society, 2002)
2002
Earlier work this paper cites.
Benjamin Rahn, Andrew C. Doherty, and Hideo Mabuchi, “Exact Performance of Concatenated Quantum Codes,” Phys. Rev. A 66
2002
Earlier work this paper cites.
Panos Aliferis, Daniel Gottesman, and John Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quant. Inf. Comput. 6
2006
Earlier work this paper cites.
J. Fern, J. Kempe, S. N. Simic, and S. Sastry, “Generalized performance of concatenated quantum codes — a dynamical systems approach,” IEEE Transactions on Automatic Control 51
2006
Earlier work this paper cites.
David Poulin, “Optimal and efficient decoding of concatenated quantum block codes,” Phys. Rev. A 74
2006
Earlier work this paper cites.

Similar

P. Aliferis and A. W. Cross, “Subsystem fault tolerance with the Bacon-Shor code,” Phys. Rev. Lett. 98
2007
Cited alongside, same era.
E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Randomized benchmarking of quantum gates,” Phys. Rev. A 77
Original
2008
Cited alongside, same era.
Andrew S. Fletcher, Peter W. Shor, and Moe Z. Win, “Structured near-optimal channel-adapted quantum error correction,” Phys. Rev. A 77
Original
2008
Cited alongside, same era.
David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg, “Surface code quantum computing with error rates over 1%,” Phys. Rev. A 83
Original
2011
Cited alongside, same era.
Bei Zeng, Andrew Cross, and Isaac L Chuang, “Transversality versus universality for additive quantum codes,” IEEE Transactions on Information Theory 57

Then

Mauricio Gutiérrez and Kenneth R. Brown, “Comparison of a quantum error-correction threshold for exact and approximate errors,” Phys. Rev. A 91
Original
2015
Later among the works it cites.
Mauricio Gutiérrez, Conor Smith, Livia Lulushi, Smitha Janardan, and Kenneth R. Brown, “Errors and pseudo-thresholds for incoherent and coherent noise,” Phys. Rev. A 94
Original
2016
Later among the works it cites.
Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz, “Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography,” Nature Communications 8
Original
2016
Later among the works it cites.
Richard Kueng, David M. Long, Andrew C. Doherty, and Steven T. Flammia, “Comparing experiments to the fault-tolerance threshold,” Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2011

Cited alongside, same era.

Easwar Magesan, Jay M. Gambetta, and Joseph Emerson, “Characterizing quantum gates via randomized benchmarking,” Phys. Rev. A 85

Original

2012

Cited alongside, same era.

Mauricio Gutiérrez, Lukas Svec, Alexander Vargo, and Kenneth R. Brown, “Approximation of realistic errors by Clifford channels and Pauli measurements,” Phys. Rev. A 87

Original

2013

Cited alongside, same era.

John Watrous, “Simpler semidefinite programs for completely bounded norms,” Chicago J. Theo. Comp. Sci. 2013

Original

2013

Cited alongside, same era.

Markus Grassl and Martin Roetteler, “Leveraging automorphisms of quantum codes for fault-tolerant quantum computation,” in Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on (IEEE, 2013) pp. 534–538, arXiv:1302.1035

Original

2013

Cited alongside, same era.

Easwar Magesan, Daniel Puzzuoli, Christopher E Granade, and David G Cory, “Modeling quantum noise for efficient testing of fault-tolerant circuits,” Physical Review A 87

2013

Cited alongside, same era.

Daniel Puzzuoli, Christopher Granade, Holger Haas, Ben Criger, Easwar Magesan, and D. G. Cory, “Tractable simulation of error correction with honest approximations to realistic fault models,” Phys. Rev. A 89

Original

2014

Cited alongside, same era.

Joel J. Wallman and Steven T. Flammia, “Randomized benchmarking with confidence,” New J. Phys. 16

Original

2014

Cited alongside, same era.

Naomi H Nickerson, “Error correcting power of small topological codes,” (2016), arXiv:1609.01753

Original