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Logical gates constitute the building blocks of fault-tolerant quantum computation.
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P. Webster and S. D. Bartlett, Fault-tolerant quantum gates with defects in topological stabilizer codes, Physical Review A 102
2020
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M. Hanks, M. P. Estarellas, W. J. Munro, and K. Nemoto, Effective compression of quantum braided circuits aided by zx-calculus, Physical Review X 10
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M. Newman, L. A. de Castro, and K. R. Brown, Generating fault-tolerant cluster states from crystal structures, Quantum 4
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For example, the 2D color code (which is locally equivalent to two copies of the surface code code Bombin et al. 2012b ) has a symmetry group containing 72 elements Yoshida 2015 ; Scruby and Browne 2020 , compared to the ℤ 2 \mathbbm{Z}_{2} symmetry of a single surface code
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F. H. Watson and S. D. Barrett, Logical error rate scaling of the toric code, New Journal of Physics 16
2014
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2020
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In condensed matter language, this check operator group can be understood as a ℤ 2 × ℤ 2 \mathbbm{Z}_{2}\times\mathbbm{Z}_{2} 1-form symmetry Gaiotto et al. 2015 ; Kapustin and Thorngren 2017 ; Roberts and Bartlett 2020
2020
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2020
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N. de Beaudrap and D. Horsman, The zx calculus is a language for surface code lattice surgery, Quantum 4
2020
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A potentially related observation is found in Ref. Farrelly et al. 2020 for a different family of codes, whereby different logical qubits can be decoded independently while remaining nearly globally optimal
2020
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I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, et al. , Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization, Quantum 4
2020
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2020
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A. Krishna and D. Poulin, Topological wormholes: Nonlocal defects on the toric code, Physical Review Research 2
2020
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T. Scruby and D. Browne, A hierarchy of anyon models realised by twists in stacked surface codes, Quantum 4
2020
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S. Roberts and S. D. Bartlett, Symmetry-protected self-correcting quantum memories, Physical Review X 10
2020
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2020
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2021
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M. E. Beverland, A. Kubica, and K. M. Svore, Cost of universality: A comparative study of the overhead of state distillation and code switching with color codes, PRX Quantum 2
2021
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2021
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L. Egan, D. M. Debroy, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Newman, M. Li, K. R. Brown, M. Cetina, et al. , Fault-tolerant control of an error-corrected qubit, Nature 598
2021
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M. B. Hastings, J. Haah, and R. O’Donnell, in Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (2021) pp. 1276–1288
2021
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M. B. Hastings and J. Haah, Dynamically generated logical qubits, Quantum 5
2021
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A. Krishna and D. Poulin, Fault-tolerant gates on hypergraph product codes, Physical Review X 11
2021
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I. H. Kim, Y.-H. Liu, S. Pallister, W. Pol, S. Roberts, and E. Lee, Fault-tolerant resource estimate for quantum chemical simulations: Case study on li-ion battery electrolyte molecules, Phys. Rev. Research 4
2022
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2022
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S. Bartolucci, P. Birchall, H. Bombin, H. Cable, C. Dawson, M. Gimeno-Segovia, E. Johnston, K. Kieling, N. Nickerson, M. Pant, et al. , Fusion-based quantum computation, Nature Communications 14
2023
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In Ref. Bartolucci et al. 2023 this group is termed the fusion group and denoted F F . It is renamed the measurement group ℳ \mathcal{M} here to note the inclusion of single-qubit measurements when required
2023
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