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Magic state distillation and the Shor factoring algorithm make essential use of logical diagonal gates.
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E. T. Campbell and M. Howard, “Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost,” Physical Review A , vol. 95, no. 2, p. 022316, 2017
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2012
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H. Anwar, E. T. Campbell, and D. E. Browne, “Qutrit magic state distillation,” New Journal of Physics , vol. 14, no. 6, p. 063006, 2012
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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, p. 041021, 2012
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2013
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I. Bengtsson, K. Blanchfield, E. Campbell, and M. Howard, “Order 3 symmetry in the Clifford hierarchy,” Journal of Physics A: Mathematical and Theoretical , vol. 47, no. 45, p. 455302, 2014
2014
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J. T. Anderson, G. Duclos-Cianci, and D. Poulin, “Fault-tolerant conversion between the steane and Reed-Muller quantum codes,” Physical review letters , vol. 113, no. 8, p. 080501, 2014
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S. X. Cui, D. Gottesman, and A. Krishna, “Diagonal gates in the Clifford hierarchy,” Physical Review A , vol. 95, no. 1, p. 012329, 2017
2017
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2019
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C. Vuillot and N. P. Breuckmann, “Quantum pin codes,” arXiv preprint arXiv:1906.11394 , 2019
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T. Pllaha, N. Rengaswamy, O. Tirkkonen, and R. Calderbank, “Un-weyl-ing the Clifford hierarchy,” Quantum , vol. 4, p. 370, 2020
2020
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2020
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N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, “On optimality of CSS codes for transversal T T ,” IEEE Journal on Selected Areas in Information Theory , vol. 1, no. 2, pp. 499–514, 2020
2020
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2021
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