Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems

Jack Edmonds, “Paths, trees, and flowers,” Canad. J. Math. 17

1965

Earlier work this paper cites.

Joan S. Birman, “On braid groups,” Comm. Pure App. Math. 22

1969

Earlier work this paper cites.

Richard M. Karp, “Reducibility among combinatorial problems,” in Complexity of Computer Computations, Proc. Sympos. IBM Thomas J. Watson Res. Center (Plenum, New York, 1972) pp. 85–103

1972

Earlier work this paper cites.

S. Micali and V. Vazirani, “An O ⁡ ( | V | ​ | E | ) O(\sqrt{|V|}|E|) algorithm for finding maximum matching in general graphs,” in Proc. 21st Ann. Symp. Found. Comp. Sci. (IEEE, 1980) pp. 17–27

1980

Earlier work this paper cites.

Sergey Bravyi and Barbara Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes,” New J. Phys. 11

Original

1983

Earlier work this paper cites.

R. Willett, J. P. Eisenstein, H. L. Störmer, D. C. Tsui, A. C. Gossard, and J. H. English, “Observation of an even-denominator quantum number in the fractional quantum Hall effect,” Phys. Rev. Lett. 59

1987

Earlier work this paper cites.

F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990)

1990

Earlier work this paper cites.

X. G. Wen and Q. Niu, “Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces,” Phys. Rev. B 41

1990

Earlier work this paper cites.

Torbjörn Einarsson, “Fractional statistics on a torus,” Phys. Rev. Lett. 64

1990

Earlier work this paper cites.

Gregory Moore and Nicholas Read, “Nonabelions in the fractional quantum Hall effect,” Nucl. Phys. B 360

1991

Earlier work this paper cites.

Yasuhiro Hatsugai, Mahito Kohmoto, and Yong-Shi Wu, “Braid groups, anyons and gauge invariance: On topologically nontrivial surfaces,” Prog. Theor. Phys. Supp. 107

1992

Earlier work this paper cites.

Chetan Nayak and Frank Wilczek, “ 2 ​ n 2n -quasihole states realize 2 ​ n − 1 2n-1 -dimensional spinor braiding statistics in paired quantum Hall states,” Nucl. Phys. B 479

1996

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.

L. Lehman, D. Ellinas, and G.K. Brennen, “Quantum walks of S ​ U ​ ( 2 ) k SU(2)_{k} anyons on a ladder,” J. Comput. Theor. Nanosci. 10

Original

1999

Earlier work this paper cites.

Daniel Gottesman, “The Heisenberg representation of quantum computers,” in Group22: Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics , edited by S. P. Corney, R. Delbourgo, and P. D. Jarvis (International Press, Cambridge, MA, 1999) pp. 32–43, arXiv:quant-ph/9807006

1999

Earlier work this paper cites.

Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill, “Topological quantum memory,” J. Math. Phys. 43

2002

Earlier work this paper cites.

A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303

2003

Earlier work this paper cites.

Michael A. Levin and Xiao-Gang Wen, “String-net condensation: A physical mechanism for topological phases,” Phys. Rev. B 71

2005

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.

Alexei Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. 321

2006

Cited alongside, same era.

Sergey Bravyi, “Universal quantum computation with the ν = 5 2 \nu=\frac{5}{2} fractional quantum Hall state,” Phys. Rev. A 73

2006

Cited alongside, same era.

Michael Freedman, Chetan Nayak, and Kevin Walker, “Towards universal topological quantum computation in the ν = 5 2 \nu=\frac{5}{2} fractional quantum Hall state,” Phys. Rev. B 73

2006

Cited alongside, same era.

Sergey Bravyi and Robert Raussendorf, “Measurement-based quantum computation with the toric code states,” Phys. Rev. A 76

2007

Cited alongside, same era.

Masaki Oshikawa, Yong Baek Kim, Kirill Shtengel, Chetan Nayak, and Sumanta Tewari, “Topological degeneracy of non-Abelian states for dummies,” Ann. Phys 322

2007

Cited alongside, same era.

Jeongwan Haah and John Preskill, “Logical-operator tradeoff for local quantum codes,” Phys. Rev. A 86

Original

2012

Later among the works it cites.

N. E. Bonesteel and D. P. DiVincenzo, “Quantum circuits for measuring Levin-Wen operators,” Phys. Rev. B 86

Original

2012

Later among the works it cites.

Robert N. C. Pfeifer, Oliver Buerschaper, Simon Trebst, Andreas W. W. Ludwig, Matthias Troyer, and Guifre Vidal, “Translation invariance, topology, and protection of criticality in chains of interacting anyons,” Phys. Rev. B 86

Original

2012

Later among the works it cites.

Austin G. Fowler, Adam C. Whiteside, and Lloyd C. L. Hollenberg, “Towards practical classical processing for the surface code,” Phys. Rev. Lett. 108

Original

2012

Later among the works it cites.

Spyridon Michalakis and Justyna P. Zwolak, “Stability of frustration-free Hamiltonians,” Comm. Math. Phys. 322