Built on

Y. H. Lin and S. H. Shao, “Anomalies and Bounds on Charged Operators,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
J. A. Harvey, Y. Hu and Y. Wu, “Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories,” J. Phys. A 53
Original
1912
Earlier work this paper cites.
E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B 300
1988
Earlier work this paper cites.
G. Moore and N. Seiberg, “Classical and quantum conformal field theory,” Comm. Math. Phys. 123(2): 177-254 (1989)
1989
Earlier work this paper cites.
L. Dolan, P. Goddard and P. Montague, “Conformal field theories, representations and lattice constructions,” Communications in mathematical physics 179 (1996) 61
1996
Earlier work this paper cites.
A. Kitaev, “Quantum computations: algorithms and error correction,” Russ. Math. Surv. 52
1997
Earlier work this paper cites.
D. Gottesman, “A Theory of fault tolerant quantum computation,” Phys. Rev. A 57
1998
Earlier work this paper cites.
A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals Phys. 303 (2003) 2-30
2003
Earlier work this paper cites.
M. Müger, “On the structure of modular categories,” Proc. London Math. Soc. 87
2003
Earlier work this paper cites.

Similar

J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators. 3. Simple currents,” Nucl. Phys. B 694
2004
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L. Wang and Z. Wang, “In and around Abelian anyon models,” J. Phys. A 53
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2004
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S. Stolz and P. Teichner, “What is an Elliptic Object?,” Lon. Math. Soc. Lec. Note Ser., 308
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2006
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Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, “Symmetries and strings of adjoint QCD 2
Original
2008
Cited alongside, same era.

Then

A. Almheiri, X. Dong and D. Harlow, “Bulk Locality and Quantum Error Correctionin AdS/CFT,” Journal of High Energy Physics, 163 (2015)
2015
Later among the works it cites.
Davydov, Alexei, “Unphysical diagonal modular invariants,” Journal of Algebra, 446 1 (2016)
2016
Later among the works it cites.
M. Buican and A. Gromov, “Anyonic Chains, Topological Defects, and Conformal Field Theory,” Commun. Math. Phys. 356
Original
2017
Later among the works it cites.
Y. Tachikawa, “TASI 2019 Lectures on Anomalies and Topological Phases.”
2019
Later among the works it cites.
C. M. Chang, Y. H. Lin, S. H. Shao, Y. Wang and X. Yin, “Topological Defect Lines and Renormalization Group Flows in Two Dimensions,” JHEP 01
Original
2019
Later among the works it cites.

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2021

Quantum Codes, CFTs, and Defects

Buican, Matthew, Dymarsky, Anatoly, Radhakrishnan, Rajath

Understand

We give a general construction relating Narain rational conformal field theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum stabilizer codes.

Starting from an abelian CS theory with a fusion group consisting of $n$ even-order factors, we map a boundary RCFT to an $n$-qubit quantum code.
When the relevant 't Hooft anomalies vanish, we can orbifold our RCFTs and describe this gauging at the level of the code.
Along the way, we give CFT interpretations of the code subspace and the Hilbert space of qubits while mapping error operations to CFT defect fields.

Built on

Y. H. Lin and S. H. Shao, “Anomalies and Bounds on Charged Operators,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
J. A. Harvey, Y. Hu and Y. Wu, “Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories,” J. Phys. A 53
Original
1912
Earlier work this paper cites.
E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B 300
1988
Earlier work this paper cites.
G. Moore and N. Seiberg, “Classical and quantum conformal field theory,” Comm. Math. Phys. 123(2): 177-254 (1989)
1989
Earlier work this paper cites.
L. Dolan, P. Goddard and P. Montague, “Conformal field theories, representations and lattice constructions,” Communications in mathematical physics 179 (1996) 61
1996
Earlier work this paper cites.
A. Kitaev, “Quantum computations: algorithms and error correction,” Russ. Math. Surv. 52
1997
Earlier work this paper cites.
D. Gottesman, “A Theory of fault tolerant quantum computation,” Phys. Rev. A 57
1998
Earlier work this paper cites.
A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals Phys. 303 (2003) 2-30
2003
Earlier work this paper cites.
M. Müger, “On the structure of modular categories,” Proc. London Math. Soc. 87
2003
Earlier work this paper cites.

Similar

J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators. 3. Simple currents,” Nucl. Phys. B 694
2004
Cited alongside, same era.
L. Wang and Z. Wang, “In and around Abelian anyon models,” J. Phys. A 53
Original
2004
Cited alongside, same era.
S. Stolz and P. Teichner, “What is an Elliptic Object?,” Lon. Math. Soc. Lec. Note Ser., 308
2004
Cited alongside, same era.
A. Maloney and E. Witten, “Averaging over Narain moduli space,” JHEP , 187 (2020) doi:10.1007/JHEP10(2020)187 [arXiv:2006.04855 [hep-th]]
Original
2006
Cited alongside, same era.
Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, “Symmetries and strings of adjoint QCD 2
Original
2008
Cited alongside, same era.

Then

A. Almheiri, X. Dong and D. Harlow, “Bulk Locality and Quantum Error Correctionin AdS/CFT,” Journal of High Energy Physics, 163 (2015)
2015
Later among the works it cites.
Davydov, Alexei, “Unphysical diagonal modular invariants,” Journal of Algebra, 446 1 (2016)
2016
Later among the works it cites.
M. Buican and A. Gromov, “Anyonic Chains, Topological Defects, and Conformal Field Theory,” Commun. Math. Phys. 356
Original
2017
Later among the works it cites.
Y. Tachikawa, “TASI 2019 Lectures on Anomalies and Topological Phases.”
2019
Later among the works it cites.
C. M. Chang, Y. H. Lin, S. H. Shao, Y. Wang and X. Yin, “Topological Defect Lines and Renormalization Group Flows in Two Dimensions,” JHEP 01
Original
2019
Later among the works it cites.