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A defining feature of topologically ordered states of matter is the existence of locally indistinguishable states on spaces with non-trivial topology.
E. H. Lieb and D. W. Robinson, in Statistical Mechanics (Springer, Berlin, Heidelberg, Berlin, Heidelberg, 1972) pp. 425–431
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This follows from Vafa’s theorem Vafa 1988 , which states that the topological spins are always rational numbers
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Qubit permutation was also extensively studied in depth by Ref. Zeng et al. 2011 in the context of stabilizer codes, despite the fact that it was realized that universal gate sets cannot be achieved even with the addition of such permutations
2011
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N. E. Bonesteel and D. P. DiVincenzo, Quantum circuits for measuring Levin-Wen operators, Phys. Rev. B 86
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2017
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H. Kaufmann, T. Ruster, C. T. Schmiegelow, M. A. Luda, V. Kaushal, J. Schulz, D. von Lindenfels, F. Schmidt-Kaler, and U. G. Poschinger, Scalable Creation of Long-Lived Multipartite Entanglement, Phys. Rev. Lett. 119
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2017
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N. M. Linke, D. Maslov, M. Roetteler, S. Debnath, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, Experimental Comparison of Two Quantum Computing Architectures, PNAS 13, 3305–3310 (2017)
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2017
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2017
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2017
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R. K. Naik, N. Leung, S. Chakram, P. Groszkowski, Y. Lu, N. Earnest, D. C. McKay, J. Koch, and D. I. Schuster, Random access quantum information processors using multimode circuit quantum electrodynamics, Nat. Commun. 1-7 (2017)
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2018
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2018
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W. Feng, N. E. Bonesteel, and D. P. DiVincenzo, Non-abelian errors in the fibonacci levin-wen model, (2018), in preparation
2018
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