Built on

H. Nishimori, Internal energy, specific heat and correlation function of the bond-random ising model, Journal of the Physical Society of Japan 66
1981
Earlier work this paper cites.
H. Nishimori, Geometry induced phase transition in the ± \pm j ising model, Journal of the Physical Society of Japan 55
1986
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54
1996
Earlier work this paper cites.
A. M. Steane, Simple quantum error-correcting codes, Phys. Rev. A 54
1996
Earlier work this paper cites.
B. Schumacher and M. A. Nielsen, Quantum data processing and error correction, Physical Review A 54
1996
Earlier work this paper cites.
D. Gottesman, Stabilizer codes and quantum error correction (1997), arXiv:quant-ph/9705052 [quant-ph]
1997
Earlier work this paper cites.
D. P. DiVincenzo, P. W. Shor, and J. A. Smolin, Quantum-channel capacity of very noisy channels, Physical Review A 57
1998
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph]
1998
Earlier work this paper cites.
I. A. Gruzberg, N. Read, and A. W. W. Ludwig, Random-bond ising model in two dimensions: The nishimori line and supersymmetry, Phys. Rev. B 63
2001
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.
H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Phys. Rev. Lett. 97
2006
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
2009
Earlier work this paper cites.
M. Ohzeki, Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices, Physical Review E 80
2009
Earlier work this paper cites.
M. M. Wilde, Logical operators of quantum codes, Physical Review A 79
2009
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Phys. Rev. A 83
2011
Earlier work this paper cites.

Similar

A. J. Landahl, J. T. Anderson, and P. R. Rice, Fault-tolerant quantum computing with color codes (2011), arXiv:1108.5738 [quant-ph]
Original
2011
Cited alongside, same era.
H. Bombin, An introduction to topological quantum codes (2013), arXiv:1311.0277 [quant-ph]
Original
2013
Cited alongside, same era.
S. Bravyi and M. B. Hastings, Homological product codes (2013), arXiv:1311.0885 [quant-ph]
Original
2013
Cited alongside, same era.
A. A. Kovalev and L. P. Pryadko, Spin glass reflection of the decoding transition for quantum error correcting codes (2014), arXiv:1311.7688 [quant-ph]
Original
2014
Cited alongside, same era.
A. Kubica, B. Yoshida, and F. Pastawski, Unfolding the color code, New Journal of Physics 17

Then

P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes (2022), arXiv:2111.03654 [cs.IT]
Original
2022
Later among the works it cites.
I. Dinur, M.-H. Hsieh, T.-C. Lin, and T. Vidick, Good Quantum LDPC Codes with Linear Time Decoders, arXiv e-prints , arXiv:2206.07750 (2022) , arXiv:2206.07750 [quant-ph]
Original
2022
Later among the works it cites.
R. Fan, Y. Bao, E. Altman, and A. Vishwanath, Diagnostics of mixed-state topological order and breakdown of quantum memory (2023), arXiv:2301.05689 [quant-ph]
Original
2023
Later among the works it cites.
J. Y. Lee, C.-M. Jian, and C. Xu, Quantum criticality under decoherence or weak measurement, PRX Quantum 4
2023
Later among the works it cites.
Y. Bao, R. Fan, A. Vishwanath, and E. Altman, Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions (2023), arXiv:2301.05687 [quant-ph]

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Reading the bibliography…

2024

Coherent information for CSS codes under decoherence

Niwa, Ryotaro, Lee, Jong Yeon

Understand

Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC).

Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons.
Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state.
Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models.

Built on

H. Nishimori, Internal energy, specific heat and correlation function of the bond-random ising model, Journal of the Physical Society of Japan 66
1981
Earlier work this paper cites.
H. Nishimori, Geometry induced phase transition in the ± \pm j ising model, Journal of the Physical Society of Japan 55
1986
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54
1996
Earlier work this paper cites.
A. M. Steane, Simple quantum error-correcting codes, Phys. Rev. A 54
1996
Earlier work this paper cites.
B. Schumacher and M. A. Nielsen, Quantum data processing and error correction, Physical Review A 54
1996
Earlier work this paper cites.
D. Gottesman, Stabilizer codes and quantum error correction (1997), arXiv:quant-ph/9705052 [quant-ph]
1997
Earlier work this paper cites.
D. P. DiVincenzo, P. W. Shor, and J. A. Smolin, Quantum-channel capacity of very noisy channels, Physical Review A 57
1998
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph]
1998
Earlier work this paper cites.
I. A. Gruzberg, N. Read, and A. W. W. Ludwig, Random-bond ising model in two dimensions: The nishimori line and supersymmetry, Phys. Rev. B 63
2001
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.
H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Phys. Rev. Lett. 97
2006
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
2009
Earlier work this paper cites.
M. Ohzeki, Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices, Physical Review E 80
2009
Earlier work this paper cites.
M. M. Wilde, Logical operators of quantum codes, Physical Review A 79
2009
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Phys. Rev. A 83
2011
Earlier work this paper cites.

Similar

A. J. Landahl, J. T. Anderson, and P. R. Rice, Fault-tolerant quantum computing with color codes (2011), arXiv:1108.5738 [quant-ph]
Original
2011
Cited alongside, same era.
H. Bombin, An introduction to topological quantum codes (2013), arXiv:1311.0277 [quant-ph]
Original
2013
Cited alongside, same era.
S. Bravyi and M. B. Hastings, Homological product codes (2013), arXiv:1311.0885 [quant-ph]
Original
2013
Cited alongside, same era.
A. A. Kovalev and L. P. Pryadko, Spin glass reflection of the decoding transition for quantum error correcting codes (2014), arXiv:1311.7688 [quant-ph]
Original
2014
Cited alongside, same era.
A. Kubica, B. Yoshida, and F. Pastawski, Unfolding the color code, New Journal of Physics 17

Then

P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes (2022), arXiv:2111.03654 [cs.IT]
Original
2022
Later among the works it cites.
I. Dinur, M.-H. Hsieh, T.-C. Lin, and T. Vidick, Good Quantum LDPC Codes with Linear Time Decoders, arXiv e-prints , arXiv:2206.07750 (2022) , arXiv:2206.07750 [quant-ph]
Original
2022
Later among the works it cites.
R. Fan, Y. Bao, E. Altman, and A. Vishwanath, Diagnostics of mixed-state topological order and breakdown of quantum memory (2023), arXiv:2301.05689 [quant-ph]
Original
2023
Later among the works it cites.
J. Y. Lee, C.-M. Jian, and C. Xu, Quantum criticality under decoherence or weak measurement, PRX Quantum 4
2023
Later among the works it cites.
Y. Bao, R. Fan, A. Vishwanath, and E. Altman, Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions (2023), arXiv:2301.05687 [quant-ph]

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2015

Cited alongside, same era.

S. Vijay, J. Haah, and L. Fu, Fracton topological order, generalized lattice gauge theory, and duality, Phys. Rev. B 94

2016

Cited alongside, same era.

N. P. Breuckmann and B. M. Terhal, Constructions and noise threshold of hyperbolic surface codes, IEEE Transactions on Information Theory 62

2016

Cited alongside, same era.

M. Mueller, D. A. Johnston, and W. Janke, Exact solutions to plaquette ising models with free and periodic boundaries, Nuclear Physics B 914

2017

Cited alongside, same era.

A. Kubica, M. E. Beverland, F. Brandão, J. Preskill, and K. M. Svore, Three-dimensional color code thresholds via statistical-mechanical mapping, Physical Review Letters 120

2018

Cited alongside, same era.

A. Kubica and B. Yoshida, Ungauging quantum error-correcting codes (2018), arXiv:1805.01836 [quant-ph]

Original

2018

Cited alongside, same era.

W. Shirley, K. Slagle, Z. Wang, and X. Chen, Fracton models on general three-dimensional manifolds, Physical Review X 8

2018

Cited alongside, same era.

A. A. Kovalev, S. Prabhakar, I. Dumer, and L. P. Pryadko, Numerical and analytical bounds on threshold error rates for hypergraph-product codes, Physical Review A 97

2018

Cited alongside, same era.

Original

2023

Later among the works it cites.

Z. Wang, Z. Wu, and Z. Wang, Intrinsic mixed-state topological order without quantum memory (2023), arXiv:2307.13758 [quant-ph]

Original

2023

Later among the works it cites.

Y. Guo and Y. Ashida, Two-dimensional symmetry-protected topological phases and transitions in open quantum systems (2023), arXiv:2311.12619 [quant-ph]

Original

2023