Built on

B. Delaunay, “Sur la sphère vide,” Bulletin de l’Académie des Sciences de l’URSS, Classe des Sciences Mathématiques et Naturelles
Original
1938
Earlier work this paper cites.
J. Edmonds, “Paths, Trees, and Flowers,” Canadian Journal of Mathematics , 17
1965
Earlier work this paper cites.
M. I. Shamos and D. Hoey, “Geometric intersection problems,” in 17th Annual Symposium on Foundations of Computer Science (sfcs 1976)
1976
Earlier work this paper cites.
New York, NY: Springer New York, , New York, NY(1985)
F. P. Preparata and M. I. Shamos, Computational Geometry · 1985
Earlier work this paper cites.
P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Physical Review A , 52
1995
Earlier work this paper cites.
A. M. Steane, “Error Correcting Codes in Quantum Theory,” Physical Review Letters , 77
1996
Earlier work this paper cites.
A. Steane, “Multiple-particle interference and quantum error correction,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences , 452
1996
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Physical Review A , 54
1996
Earlier work this paper cites.
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Physical Review A , 54
1996
Earlier work this paper cites.
E. Knill, R. Laflamme, and W. H. Zurek, “Resilient Quantum Computation: Error Models and Thresholds,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 454
1997
Earlier work this paper cites.
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” Journal of Mathematical Physics , 43
2002
Earlier work this paper cites.
A. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics , 303
2003
Earlier work this paper cites.
C. Wang, J. Harrington, and J. Preskill, “Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory,” Annals of Physics , 303
2003
Earlier work this paper cites.
PhD thesis, (2004)
J. Harrington, Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes · 2004
Earlier work this paper cites.
P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Information and Computation
2005
Earlier work this paper cites.
D. Poulin, “Stabilizer Formalism for Operator Quantum Error Correction,” Physical Review Letters , 95
2005
Earlier work this paper cites.
K. Takeda, T. Sasamoto, and H. Nishimori, “Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture,” Journal of Physics A: Mathematical and General , 38
2005
Earlier work this paper cites.
M. Hinczewski and A. N. Berker, “Multicritical point relations in three dual pairs of hierarchical-lattice Ising spin glasses,” Physical Review B , 72
2005
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, “Topological Quantum Distillation,” Physical Review Letters , 97
2006
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, “Topological Computation without Braiding,” Physical Review Letters , 98
2007
Earlier work this paper cites.
V. Murg, F. Verstraete, and J. I. Cirac, “Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states,” Physical Review A , 75
2007
Earlier work this paper cites.
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix Product State Representations,” Quantum Information & Computation
2007
Earlier work this paper cites.
H. Nishimori, “Duality in Finite-Dimensional Spin Glasses,” Journal of Statistical Physics , 126
2007
Earlier work this paper cites.
D. Aharonov and M. Ben-Or, “Fault-Tolerant Quantum Computation with Constant Error Rate,” SIAM Journal on Computing , 38
2008
Earlier work this paper cites.
M. Ohzeki, “Locations of multicritical points for spin glasses on regular lattices,” Physical Review E , 79
Original
2009
Earlier work this paper cites.
H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, “Error Threshold for Color Codes and Random Three-Body Ising Models,” Physical Review Letters , 103
Original
2009
Earlier work this paper cites.
D. S. Wang, A. G. Fowler, C. D. Hill, and L. C. Hollenberg, “Graphical algorithms and threshold error rates for the 2d color code,” Quantum Information and Computation
Original
2010
Earlier work this paper cites.
G. Duclos-Cianci and D. Poulin, “Fast Decoders for Topological Quantum Codes,” Physical Review Letters , 104
Original
2010
Earlier work this paper cites.

Similar

Cambridge University Press, Cambridge, (2011)
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information 10th Anniversary Edition · 2011
Cited alongside, same era.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Physical Review A , 86
Original
2012
Cited alongside, same era.
H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes,” New Journal of Physics , 14
Original
2012
Cited alongside, same era.
H. Bombin, R. S. Andrist, M. Ohzeki, H. G. Katzgraber, and M. A. Martin-Delgado, “Strong Resilience of Topological Codes to Depolarization,” Physical Review X , 2
Original
2012
Cited alongside, same era.
J. R. Wootton and D. Loss, “High Threshold Error Correction for the Surface Code,” Physical Review Letters , 109

Then

S. Krastanov and L. Jiang, “Deep Neural Network Probabilistic Decoder for Stabilizer Codes,” Scientific Reports , 7
2017
Later among the works it cites.
N. Delfosse and N. H. Nickerson, “Almost-linear time decoding algorithm for topological codes,” arXiv:1709.06218 , (2017)
Original
2017
Later among the works it cites.
B. Criger and I. Ashraf, “Multi-path Summation for Decoding 2D Topological Codes,” pp. 1–18, arXiv:1709.02154 , (2017)
Original
2017
Later among the works it cites.
A. S. Darmawan and D. Poulin, “Tensor-Network Simulations of the Surface Code under Realistic Noise,” Physical Review Letters , 119
Original
2017
Later among the works it cites.
J. C. Bridgeman and C. T. Chubb, “Hand-waving and interpretive dance: an introductory course on tensor networks,” Journal of Physics A: Mathematical and Theoretical , 50

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2021

General tensor network decoding of 2D Pauli codes

Chubb, Christopher T.

Understand

In this work we develop a general tensor network decoder for 2D codes.

Specifically, we propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise.
For a code consisting of $n$ qubits our decoder has a runtime of $O(n\log n+n\chi^3)$, where $\chi$ is an approximation parameter.
We numerically demonstrate the power of this decoder by studying four classes of codes under three noise models, namely regular surface codes, irregular surface codes, subsystem surface codes and colour codes, under bit-flip, phase-flip and depolarising noise.

Built on

B. Delaunay, “Sur la sphère vide,” Bulletin de l’Académie des Sciences de l’URSS, Classe des Sciences Mathématiques et Naturelles
Original
1938
Earlier work this paper cites.
J. Edmonds, “Paths, Trees, and Flowers,” Canadian Journal of Mathematics , 17
1965
Earlier work this paper cites.
M. I. Shamos and D. Hoey, “Geometric intersection problems,” in 17th Annual Symposium on Foundations of Computer Science (sfcs 1976)
1976
Earlier work this paper cites.
New York, NY: Springer New York, , New York, NY(1985)
F. P. Preparata and M. I. Shamos, Computational Geometry · 1985
Earlier work this paper cites.
P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Physical Review A , 52
1995
Earlier work this paper cites.
A. M. Steane, “Error Correcting Codes in Quantum Theory,” Physical Review Letters , 77
1996
Earlier work this paper cites.
A. Steane, “Multiple-particle interference and quantum error correction,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences , 452
1996
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Physical Review A , 54
1996
Earlier work this paper cites.
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Physical Review A , 54
1996
Earlier work this paper cites.
E. Knill, R. Laflamme, and W. H. Zurek, “Resilient Quantum Computation: Error Models and Thresholds,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 454
1997
Earlier work this paper cites.
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” Journal of Mathematical Physics , 43
2002
Earlier work this paper cites.
A. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics , 303
2003
Earlier work this paper cites.
C. Wang, J. Harrington, and J. Preskill, “Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory,” Annals of Physics , 303
2003
Earlier work this paper cites.
PhD thesis, (2004)
J. Harrington, Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes · 2004
Earlier work this paper cites.
P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Information and Computation
2005
Earlier work this paper cites.
D. Poulin, “Stabilizer Formalism for Operator Quantum Error Correction,” Physical Review Letters , 95
2005
Earlier work this paper cites.
K. Takeda, T. Sasamoto, and H. Nishimori, “Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture,” Journal of Physics A: Mathematical and General , 38
2005
Earlier work this paper cites.
M. Hinczewski and A. N. Berker, “Multicritical point relations in three dual pairs of hierarchical-lattice Ising spin glasses,” Physical Review B , 72
2005
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, “Topological Quantum Distillation,” Physical Review Letters , 97
2006
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, “Topological Computation without Braiding,” Physical Review Letters , 98
2007
Earlier work this paper cites.
V. Murg, F. Verstraete, and J. I. Cirac, “Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states,” Physical Review A , 75
2007
Earlier work this paper cites.
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix Product State Representations,” Quantum Information & Computation
2007
Earlier work this paper cites.
H. Nishimori, “Duality in Finite-Dimensional Spin Glasses,” Journal of Statistical Physics , 126
2007
Earlier work this paper cites.
D. Aharonov and M. Ben-Or, “Fault-Tolerant Quantum Computation with Constant Error Rate,” SIAM Journal on Computing , 38
2008
Earlier work this paper cites.
M. Ohzeki, “Locations of multicritical points for spin glasses on regular lattices,” Physical Review E , 79
Original
2009
Earlier work this paper cites.
H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, “Error Threshold for Color Codes and Random Three-Body Ising Models,” Physical Review Letters , 103
Original
2009
Earlier work this paper cites.
D. S. Wang, A. G. Fowler, C. D. Hill, and L. C. Hollenberg, “Graphical algorithms and threshold error rates for the 2d color code,” Quantum Information and Computation
Original
2010
Earlier work this paper cites.
G. Duclos-Cianci and D. Poulin, “Fast Decoders for Topological Quantum Codes,” Physical Review Letters , 104
Original
2010
Earlier work this paper cites.

Similar

Cambridge University Press, Cambridge, (2011)
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information 10th Anniversary Edition · 2011
Cited alongside, same era.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Physical Review A , 86
Original
2012
Cited alongside, same era.
H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes,” New Journal of Physics , 14
Original
2012
Cited alongside, same era.
H. Bombin, R. S. Andrist, M. Ohzeki, H. G. Katzgraber, and M. A. Martin-Delgado, “Strong Resilience of Topological Codes to Depolarization,” Physical Review X , 2
Original
2012
Cited alongside, same era.
J. R. Wootton and D. Loss, “High Threshold Error Correction for the Surface Code,” Physical Review Letters , 109

Then

S. Krastanov and L. Jiang, “Deep Neural Network Probabilistic Decoder for Stabilizer Codes,” Scientific Reports , 7
2017
Later among the works it cites.
N. Delfosse and N. H. Nickerson, “Almost-linear time decoding algorithm for topological codes,” arXiv:1709.06218 , (2017)
Original
2017
Later among the works it cites.
B. Criger and I. Ashraf, “Multi-path Summation for Decoding 2D Topological Codes,” pp. 1–18, arXiv:1709.02154 , (2017)
Original
2017
Later among the works it cites.
A. S. Darmawan and D. Poulin, “Tensor-Network Simulations of the Surface Code under Realistic Noise,” Physical Review Letters , 119
Original
2017
Later among the works it cites.
J. C. Bridgeman and C. T. Chubb, “Hand-waving and interpretive dance: an introductory course on tensor networks,” Journal of Physics A: Mathematical and Theoretical , 50

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

2012

Cited alongside, same era.

K. Fujii and Y. Tokunaga, “Error and loss tolerances of surface codes with general lattice structures,” Physical Review A , 86

Original

2012

Cited alongside, same era.

S. Bravyi, G. Duclos-Cianci, D. Poulin, and M. Suchara, “Subsystem surface codes with three-qubit check operators,” Quantum Information and Computation

Original

2012

Cited alongside, same era.

M. Ohzeki and K. Fujii, “Duality analysis on random planar lattices,” Physical Review E , 86

Original

2012

Cited alongside, same era.

H. Bombin, “An Introduction to Topological Quantum Codes,” arXiv:1311.0277 , (2013)

Original

2013

Cited alongside, same era.

S. Bravyi and J. Haah, “Quantum Self-Correction in the 3D Cubic Code Model,” Physical Review Letters , 111

2013

Cited alongside, same era.

G. Duclos-Cianci and D. Poulin, “Fault-Tolerant Renormalization Group Decoder for Abelian Topological Codes,” arXiv:1304.6100 , (2013)

Original

2013

Cited alongside, same era.

S. Bravyi and A. Vargo, “Simulation of rare events in quantum error correction,” Physical Review A - Atomic, Molecular, and Optical Physics , 88

Original

2013

Cited alongside, same era.

Original

2017