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With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes.
R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. , vol. 93, pp. 99–110, Jan 1954. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRev.93.99
1954
Earlier work this paper cites.
J.-P. Serre, Linear representations of finite groups . New York: Springer-Verlag, 1977
1977
Earlier work this paper cites.
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum . WORLD SCIENTIFIC, 1988. [Online]. Available: https://www.worldscientific.com/doi/abs/10.1142/0270
1988
Earlier work this paper cites.
A. Calderbank, E. Rains, P. Shor, and N. Sloane, “Quantum error correction via codes over G F ( 4 ) {GF}(4) ,” in Proceedings of IEEE International Symposium on Information Theory , 1997, pp. 292–
1997
Earlier work this paper cites.
E. Rains, “Quantum shadow enumerators,” IEEE Transactions on Information Theory , vol. 45, no. 7, pp. 2361–2366, 1999
1999
Earlier work this paper cites.
E. Rains, “Quantum codes of minimum distance two,” IEEE Transactions on Information Theory , vol. 45, no. 1, pp. 266–271, 1999
1999
Earlier work this paper cites.
H. Georgi, Lie algebras in particle physics , 2nd ed. Reading, MA: Perseus Books, 1999, vol. 54
1999
Earlier work this paper cites.
E. Knill, R. Laflamme, and L. Viola, “Theory of quantum error correction for general noise,” Physical Review Letters , vol. 84, no. 11, pp. 2525–2528, mar 2000. [Online]. Available: https://doi.org/10.1103%2Fphysrevlett.84.2525
2000
Earlier work this paper cites.
A. Thangaraj and S. McLaughlin, “Quantum codes from cyclic codes over G F ( 4 m ) {GF}(4^{m}) ,” IEEE Transactions on Information Theory , vol. 47, no. 3, pp. 1176–1178, 2001
2001
Earlier work this paper cites.
H. Pollatsek and M. B. Ruskai, “Permutationally invariant codes for quantum error correction,” Linear Algebra and its Applications , vol. 392, pp. 255–288, 2004. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0024379504002903
2004
Earlier work this paper cites.
M. Grassl and M. Rotteler, “Quantum Goethals-Preparata codes,” in 2008 IEEE International Symposium on Information Theory . IEEE, Jul. 2008. [Online]. Available: http://dx.doi.org/10.1109/ISIT.2008.4594996
2008
Earlier work this paper cites.
B. Zeng, X. Chen, and I. L. Chuang, “Semi-Clifford operations, structure of 𝒞 k \mathcal{C}_{k} hierarchy, and gate complexity for fault-tolerant quantum computation,” Physical Review A , vol. 77, no. 4, apr 2008. [Online]. Available: https://doi.org/10.1103%2Fphysreva.77.042313
2008
Earlier work this paper cites.
2009
Earlier work this paper cites.
D. B. Hume, C. W. Chou, T. Rosenband, and D. J. Wineland, “Preparation of Dicke states in an ion chain,” Phys. Rev. A , vol. 80, p. 052302, Nov 2009. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.80.052302
2009
Earlier work this paper cites.
2010
Earlier work this paper cites.
K. Wirthmüller, “Automorphisms of stabilizer codes,” 2011. [Online]. Available: arxiv:1102.5715
2011
Earlier work this paper cites.
B. Zeng, A. Cross, and I. L. Chuang, “Transversality versus universality for additive quantum codes,” IEEE Transactions on Information Theory , vol. 57, no. 9, pp. 6272–6284, 2011
2011
Earlier work this paper cites.
S. Bravyi and J. Haah, “Magic-state distillation with low overhead,” Physical Review A , vol. 86, no. 5, Nov. 2012. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.86.052329
2012
Earlier work this paper cites.
S. Roman, Fundamentals of Group Theory . Birkhäuser Boston, 2012. [Online]. Available: http://dx.doi.org/10.1007/978-0-8176-8301-6
2012
Earlier work this paper cites.
S. Bravyi and J. Haah, “Magic-state distillation with low overhead,” Physical Review A , vol. 86, no. 5, nov 2012. [Online]. Available: https://doi.org/10.1103%2Fphysreva.86.052329
2012
Cited alongside, same era.
M. Howard and J. Vala, “Qudit versions of the qubit π / 8 \pi/8 gate,” Phys. Rev. A , vol. 86, p. 022316, Aug 2012. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.86.022316
2012
Cited alongside, same era.
E. T. Campbell, H. Anwar, and D. E. Browne, “Magic-state distillation in all prime dimensions using quantum reed-muller codes,” Physical Review X , vol. 2, no. 4, Dec. 2012. [Online]. Available: http://dx.doi.org/10.1103/PhysRevX.2.041021
2012
Cited alongside, same era.
Y. Ouyang, “Permutation-invariant quantum codes,” Physical Review A , vol. 90, no. 6, Dec. 2014. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.90.062317
2014
Cited alongside, same era.
P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, “Continuous symmetries and approximate quantum error correction,” Physical Review X , vol. 10, no. 4, oct 2020. [Online]. Available: https://doi.org/10.1103%2Fphysrevx.10.041018
2020
Later among the works it cites.
M. T. Johnsson, N. R. Mukty, D. Burgarth, T. Volz, and G. K. Brennen, “Geometric pathway to scalable quantum sensing,” Physical Review Letters , vol. 125, no. 19, nov 2020. [Online]. Available: https://doi.org/10.1103%2Fphysrevlett.125.190403
2020
Later among the works it cites.
J. A. Gross, “Designing codes around interactions: The case of a spin,” Physical Review Letters , vol. 127, no. 1, jul 2021. [Online]. Available: https://doi.org/10.1103%2Fphysrevlett.127.010504
2021
Later among the works it cites.
P. Hayden, S. Nezami, S. Popescu, and G. Salton, “Error correction of quantum reference frame information,” PRX Quantum , vol. 2, no. 1, feb 2021. [Online]. Available: https://doi.org/10.1103%2Fprxquantum.2.010326
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B. Lücke, J. Peise, G. Vitagliano, J. Arlt, L. Santos, G. Tóth, and C. Klempt, “Detecting multiparticle entanglement of Dicke states,” Phys. Rev. Lett. , vol. 112, p. 155304, Apr 2014. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.112.155304
2014
Cited alongside, same era.
H. Bombín, “Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes,” New Journal of Physics , vol. 17, no. 8, p. 083002, aug 2015. [Online]. Available: https://dx.doi.org/10.1088/1367-2630/17/8/083002
2015
Cited alongside, same era.
A. Kubica and M. E. Beverland, “Universal transversal gates with color codes: A simplified approach,” Physical Review A , vol. 91, no. 3, Mar. 2015. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.91.032330
2015
Cited alongside, same era.
M. Fallbacher, “Breaking classical lie groups to finite subgroups – an automated approach,” Nuclear Physics B , vol. 898, p. 229–247, Sep. 2015. [Online]. Available: http://dx.doi.org/10.1016/j.nuclphysb.2015.07.004
2015
Cited alongside, same era.
J. T. Anderson and T. Jochym-O’Connor, “Classification of transversal gates in qubit stabilizer codes,” Quantum Information and Computation , vol. 16, p. 771–802, Jul. 2016
2016
Cited alongside, same era.
J. Haah, “Towers of generalized divisible quantum codes,” Physical Review A , vol. 97, no. 4, Apr. 2018. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.97.042327
2018
Cited alongside, same era.
J. Haah and M. B. Hastings, “Codes and protocols for distilling T T , controlled- S S , and Toffoli gates,” Quantum , vol. 2, p. 71, jun 2018. [Online]. Available: https://doi.org/10.22331%2Fq-2018-06-07-71
2018
Cited alongside, same era.
T. Jochym-O’Connor, A. Kubica, and T. J. Yoder, “Disjointness of stabilizer codes and limitations on fault-tolerant logical gates,” Physical Review X , vol. 8, no. 2, may 2018. [Online]. Available: https://doi.org/10.1103%2Fphysrevx.8.021047
2018
Cited alongside, same era.
2021
Later among the works it cites.
2021
Later among the works it cites.
Y. Wang and B. M. Terhal, “Preparing Dicke states in a spin ensemble using phase estimation,” Physical Review A , vol. 104, no. 3, sep 2021. [Online]. Available: https://doi.org/10.1103%2Fphysreva.104.032407
2021
Later among the works it cites.
2022
Later among the works it cites.
A. Bärtschi and S. Eidenbenz, “Short-depth circuits for Dicke state preparation,” in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) , 2022, pp. 87–96
2022
Later among the works it cites.
S. Aktar, A. Bartschi, A.-H. A. Badawy, and S. Eidenbenz, “A divide-and-conquer approach to Dicke state preparation,” IEEE Transactions on Quantum Engineering , vol. 3, pp. 1–16, 2022. [Online]. Available: https://doi.org/10.1109%2Ftqe.2022.3174547
2022
Later among the works it cites.
Y. Ouyang and G. K. Brennen, “Quantum error correction on symmetric quantum sensors,” 2022
2022
Later among the works it cites.
S. Omanakuttan and J. A. Gross, “Multispin Clifford codes for angular momentum errors in spin systems,” Physical Review A , vol. 108, no. 2, Aug. 2023. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.108.022424
2023
Closest in time.
E. Kubischta and I. Teixeira, “Family of quantum codes with exotic transversal gates,” Physical Review Letters , vol. 131, no. 24, Dec. 2023. [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.131.240601
2023
Closest in time.
2023
Closest in time.
E. Kubischta, Nov 2023. [Online]. Available: https://community.wolfram.com/groups/-/m/t/3073281
2023
Closest in time.
M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes,” Online available at http://www.codetables.de , 2007, accessed on 2024-09-24
2024
Closest in time.
J. T. Anderson, “On groups in the qubit Clifford hierarchy,” Quantum , vol. 8, p. 1370, Jun. 2024. [Online]. Available: http://dx.doi.org/10.22331/q-2024-06-13-1370
2024
Closest in time.
A. Aydin, M. A. Alekseyev, and A. Barg, “A family of permutationally invariant quantum codes,” Quantum , vol. 8, p. 1321, Apr. 2024. [Online]. Available: http://dx.doi.org/10.22331/q-2024-04-30-1321
2024
Closest in time.