Built on

B. J. Brown and D. J. Williamson, Parallelized quantum error correction with fracton topological codes, Physical Review Research 2
Original
1901
Earlier work this paper cites.
S. Pai and M. Hermele, Fracton fusion and statistics, Physical Review B 100
Original
1903
Earlier work this paper cites.
W. Ji and X. G. Wen, Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions, Physical Review Research 1
Original
1905
Earlier work this paper cites.
A. Prem and D. Williamson, Gauging permutation symmetries as a route to non-Abelian fractons, SciPost Physics 7
Original
1905
Earlier work this paper cites.
D. Bulmash and M. Barkeshli, Gauging fractons: Immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies, Physical Review B 100
Original
1905
Earlier work this paper cites.
A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, Sorting topological stabilizer models in three dimensions, Physical Review B 100
Original
1908
Earlier work this paper cites.
A. Dua, P. Sarkar, D. J. Williamson, and M. Cheng, Bifurcating entanglement-renormalization group flows of fracton stabilizer models, PHYSICAL REVIEW RESEARCH 2
Original
1909
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Physical Review A 83
Original
1962
Earlier work this paper cites.
X. G. Wen, Topological Orders in Rigid States, International Journal of Modern Physics B 04
1990
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.
P. W. Shor, Fault-tolerant quantum computation (1997), arxiv:quant-ph/9605011
1997
Earlier work this paper cites.
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, Quantum Error Correction and Orthogonal Geometry, Physical Review Letters 78
1997
Earlier work this paper cites.
D. E. Gottesman, Stabilizer Codes and Quantum Error Correction , Ph.D. thesis , California Institute of Technology (1997)
1997
Earlier work this paper cites.
A. Yu. Kitaev, Quantum Error Correction with Imperfect Gates, in Quantum Communication, Computing, and Measurement , edited by O. Hirota, A. S. Holevo, and C. M. Caves (Springer US, Boston, MA, 1997) pp. 181–188
1997
Earlier work this paper cites.
J. Preskill, Fault-Tolerant Quantum Computation, in Introduction to Quantum Computation and Information (WORLD SCIENTIFIC, 1998) pp. 213–269
1998
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052 (1998), arxiv:quant-ph/9811052
1998
Earlier work this paper cites.
D. Gottesman, The Heisenberg Representation of Quantum Computers, arXiv:quant-ph/9807006 (1998), arxiv:quant-ph/9807006
1998
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. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
D. J. Williamson and M. Cheng, Designer non-Abelian fractons from topological layers, Physical Review B 107
Original
2004
Earlier work this paper cites.
C. Chamon, Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection, Physical Review Letters 94
2005
Earlier work this paper cites.
D. Bacon, Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories, Physical Review A - Atomic, Molecular, and Optical Physics 73
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.
H. Bombin and M. A. Martin-Delgado, Topological Quantum Distillation, Physical Review Letters 97
2006
Earlier work this paper cites.
R. Alicki, M. Fannes, and M. Horodecki, On thermalization in Kitaev’s 2D model, Journal of Physics A: Mathematical and Theoretical 42
2009
Earlier work this paper cites.

Similar

S. Bravyi and B. Terhal, A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes, New Journal of Physics 11
2009
Cited alongside, same era.
H. Alloul, J. Bobroff, M. Gabay, and P. J. Hirschfeld, Defects in correlated metals and superconductors, Reviews of Modern Physics 81
2009
Cited alongside, same era.
R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki, On Thermal Stability of Topological Qubit in Kitaev’s 4D Model, Open Systems & Information Dynamics 17
2010
Cited alongside, same era.
S. Chesi, B. Röthlisberger, and D. Loss, Self-correcting quantum memory in a thermal environment, Physical Review A 82
2010
Cited alongside, same era.
J. Sullivan, T. Iadecola, and D. J. Williamson, Planar p-string condensation: Chiral fracton phases from fractional quantum Hall layers and beyond, Physical Review B 103
Original

Then

B. J. Brown, D. Loss, J. K. Pachos, C. N. Self, and J. R. Wootton, Quantum memories at finite temperature, Reviews of Modern Physics 88
Original
2016
Later among the works it cites.
S. Vijay, J. Haah, and L. Fu, Fracton Topological Order, Generalized Lattice Gauge Theory and Duality, Physical Review B 94
Original
2016
Later among the works it cites.
D. J. Williamson, Fractal symmetries: Ungauging the cubic code, Physical Review B 94
Original
2016
Later among the works it cites.
C. G. Brell, A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less), New Journal of Physics 18
2016
Later among the works it cites.
B. J. Brown, K. Laubscher, M. S. Kesselring, and J. R. Wootton, Poking holes and cutting corners to achieve Clifford gates with the surface code, Physical Review X 7

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Reading the bibliography…

2023

No Strings Attached: Boundaries and Defects in the Cubic Code

Aitchison, Cory T., Bulmash, Daniel, Dua, Arpit et al.

Understand

Haah's cubic code is the prototypical type-II fracton topological order.

It instantiates the no string-like operator property that underlies the favorable scaling of its code distance and logical energy barrier.
Previously, the cubic code was only explored in translation-invariant systems on infinite and periodic lattices.
In these settings, the code distance scales superlinearly with the linear system size, while the number of logical qubits within the degenerate ground space exhibits a complicated functional dependence that undergoes large fluctuations within a linear envelope.

Built on

B. J. Brown and D. J. Williamson, Parallelized quantum error correction with fracton topological codes, Physical Review Research 2
Original
1901
Earlier work this paper cites.
S. Pai and M. Hermele, Fracton fusion and statistics, Physical Review B 100
Original
1903
Earlier work this paper cites.
W. Ji and X. G. Wen, Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions, Physical Review Research 1
Original
1905
Earlier work this paper cites.
A. Prem and D. Williamson, Gauging permutation symmetries as a route to non-Abelian fractons, SciPost Physics 7
Original
1905
Earlier work this paper cites.
D. Bulmash and M. Barkeshli, Gauging fractons: Immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies, Physical Review B 100
Original
1905
Earlier work this paper cites.
A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, Sorting topological stabilizer models in three dimensions, Physical Review B 100
Original
1908
Earlier work this paper cites.
A. Dua, P. Sarkar, D. J. Williamson, and M. Cheng, Bifurcating entanglement-renormalization group flows of fracton stabilizer models, PHYSICAL REVIEW RESEARCH 2
Original
1909
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Physical Review A 83
Original
1962
Earlier work this paper cites.
X. G. Wen, Topological Orders in Rigid States, International Journal of Modern Physics B 04
1990
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.
P. W. Shor, Fault-tolerant quantum computation (1997), arxiv:quant-ph/9605011
1997
Earlier work this paper cites.
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, Quantum Error Correction and Orthogonal Geometry, Physical Review Letters 78
1997
Earlier work this paper cites.
D. E. Gottesman, Stabilizer Codes and Quantum Error Correction , Ph.D. thesis , California Institute of Technology (1997)
1997
Earlier work this paper cites.
A. Yu. Kitaev, Quantum Error Correction with Imperfect Gates, in Quantum Communication, Computing, and Measurement , edited by O. Hirota, A. S. Holevo, and C. M. Caves (Springer US, Boston, MA, 1997) pp. 181–188
1997
Earlier work this paper cites.
J. Preskill, Fault-Tolerant Quantum Computation, in Introduction to Quantum Computation and Information (WORLD SCIENTIFIC, 1998) pp. 213–269
1998
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052 (1998), arxiv:quant-ph/9811052
1998
Earlier work this paper cites.
D. Gottesman, The Heisenberg Representation of Quantum Computers, arXiv:quant-ph/9807006 (1998), arxiv:quant-ph/9807006
1998
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. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
D. J. Williamson and M. Cheng, Designer non-Abelian fractons from topological layers, Physical Review B 107
Original
2004
Earlier work this paper cites.
C. Chamon, Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection, Physical Review Letters 94
2005
Earlier work this paper cites.
D. Bacon, Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories, Physical Review A - Atomic, Molecular, and Optical Physics 73
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.
H. Bombin and M. A. Martin-Delgado, Topological Quantum Distillation, Physical Review Letters 97
2006
Earlier work this paper cites.
R. Alicki, M. Fannes, and M. Horodecki, On thermalization in Kitaev’s 2D model, Journal of Physics A: Mathematical and Theoretical 42
2009
Earlier work this paper cites.

Similar

S. Bravyi and B. Terhal, A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes, New Journal of Physics 11
2009
Cited alongside, same era.
H. Alloul, J. Bobroff, M. Gabay, and P. J. Hirschfeld, Defects in correlated metals and superconductors, Reviews of Modern Physics 81
2009
Cited alongside, same era.
R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki, On Thermal Stability of Topological Qubit in Kitaev’s 4D Model, Open Systems & Information Dynamics 17
2010
Cited alongside, same era.
S. Chesi, B. Röthlisberger, and D. Loss, Self-correcting quantum memory in a thermal environment, Physical Review A 82
2010
Cited alongside, same era.
J. Sullivan, T. Iadecola, and D. J. Williamson, Planar p-string condensation: Chiral fracton phases from fractional quantum Hall layers and beyond, Physical Review B 103
Original

Then

B. J. Brown, D. Loss, J. K. Pachos, C. N. Self, and J. R. Wootton, Quantum memories at finite temperature, Reviews of Modern Physics 88
Original
2016
Later among the works it cites.
S. Vijay, J. Haah, and L. Fu, Fracton Topological Order, Generalized Lattice Gauge Theory and Duality, Physical Review B 94
Original
2016
Later among the works it cites.
D. J. Williamson, Fractal symmetries: Ungauging the cubic code, Physical Review B 94
Original
2016
Later among the works it cites.
C. G. Brell, A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less), New Journal of Physics 18
2016
Later among the works it cites.
B. J. Brown, K. Laubscher, M. S. Kesselring, and J. R. Wootton, Poking holes and cutting corners to achieve Clifford gates with the surface code, Physical Review X 7

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2010

Cited alongside, same era.

B. Yoshida, Feasibility of self-correcting quantum memory and thermal stability of topological order, Annals of Physics 326

2011

Cited alongside, same era.

S. Bravyi, B. Leemhuis, and B. M. Terhal, Topological order in an exactly solvable 3D spin model, Annals of Physics 326

2011

Cited alongside, same era.

S. Bravyi and J. Haah, On the energy landscape of 3D spin Hamiltonians with topological order, Physical Review Letters 107

Original

2011

Cited alongside, same era.

S. Beigi, P. W. Shor, and D. Whalen, The Quantum Double Model with Boundary: Condensations and Symmetries, Communications in Mathematical Physics 306

Original

2011

Cited alongside, same era.

J. Haah and J. Preskill, Logical-operator tradeoff for local quantum codes, Physical Review A 86

2012

Cited alongside, same era.

C. Castelnovo and C. Chamon, Topological quantum glassiness, Philosophical Magazine 92

2012

Cited alongside, same era.

I. H. Kim, 3 3 D local qupit quantum code without string logical operator, arXiv , 9 (2012) , arXiv:1202.0052

Original

2012

Cited alongside, same era.

Original

2017