{"id":26222,"date":"2025-09-16T17:58:08","date_gmt":"2025-09-16T17:58:08","guid":{"rendered":"https:\/\/www.newsbeep.com\/nz\/26222\/"},"modified":"2025-09-16T17:58:08","modified_gmt":"2025-09-16T17:58:08","slug":"constant-overhead-magic-state-distillation-nature-physics","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/nz\/26222\/","title":{"rendered":"Constant-overhead magic state distillation | Nature Physics"},"content":{"rendered":"

Gottesman, D. An introduction to quantum error correction. Proc. Symp. Appl. Math. 58, 221\u2013236 (2002).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error. In Proc. Twenty-Ninth Annual ACM Symposium on Theory of Computing, STOC \u201997 176\u2013188 (Association for Computing Machinery, 1997).<\/p>\n

Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error rate. SIAM J. Comput. 38, 1207 (2008).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Shor, P. Fault-tolerant quantum computation. In Proc. 37th Conference on Foundations of Computer Science 56\u201365 (IEEE, 1996).<\/p>\n

Aliferis, P., Gottesman, D. & Preskill, J. Quantum accuracy threshold for concatenated distance-3 codes. Quantum Inf. Comput. 6, 97\u2013165 (2006).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Reichardt, B. W. in Automata, Languages and Programming (eds Bugliesi, M. et al.) 60\u201361 (Springer, 2006).<\/p>\n

Yamasaki, H. & Koashi, M. Time-efficient constant-space-overhead fault-tolerant quantum computation. Nat. Phys. 20, 247\u2013253 (2024).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58\u201365 (2024).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gupta, R. S. et al. Encoding a magic state with beyond break-even fidelity. Nature 625, 259\u2013263 (2024).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Acharya, R. et al. Quantum error correction below the surface code threshold. Nature 638, 920\u2013926 (2024).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gottesman, D. Stabilizer Codes and Quantum Error Correction, Ph.D. thesis, California Institute of Technology (1997).<\/p>\n

Eastin, B. & Knill, E. Restrictions on transversal encoded quantum gate sets. Phys. Rev. Lett. 102, 110502 (2009).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bravyi, S. & Kitaev, A. Universal quantum computation with ideal clifford gates and noisy ancillas. Phys. Rev. A 71, 022316 (2005).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Knill, E. Fault-tolerant postselected quantum computation: schemes. Preprint at https:\/\/doi.org\/10.48550\/arXiv.quant-ph\/0402171<\/a> (2004).<\/p>\n

Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390\u2013393 (1999).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bombin, H. & Martin-Delgado, M. A. Topological quantum distillation. Phys. Rev. Lett. 97, 180501 (2006).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kubica, A. & Beverland, M. E. Universal transversal gates with color codes: a simplified approach. Phys. Rev. A 91, 032330 (2015).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Moussa, J. E. Transversal clifford gates on folded surface codes. Phys. Rev. A 94, 042316 (2016).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

\u0141odyga, J., Mazurek, P., Grudka, A. & Horodecki, M. Simple scheme for encoding and decoding a qubit in unknown state for various topological codes. Sci. Rep. 5, 8975 (2015).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Li, Y. A magic state\u2019s fidelity can be superior to the operations that created it. N. J. Phys. 17, 023037 (2015).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Litinski, D. Magic state distillation: not as costly as you think. Quantum 3, 205 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gidney, C. & Eker\u00e5, M. How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum 5, 433 (2021).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bravyi, S. & Haah, J. Magic-state distillation with low overhead. Phys. Rev. A 86, 052329 (2012).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Haah, J. & Hastings, M. B. Codes and protocols for distilling t, controlled-s, and Toffoli gates. Quantum 2, 71 (2018).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Meier, A. M., Eastin, B. & Knill, E. Magic-state distillation with the four-qubit code. Quantum Inf. Comput. 13, 195\u2013209 (2013).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Campbell, E. T., Anwar, H. & Browne, D. E. Magic-state distillation in all prime dimensions using quantum reed-muller codes. Phys. Rev. X 2, 041021 (2012).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jones, C. Multilevel distillation of magic states for quantum computing. Phys. Rev. A 87, 042305 (2013).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Hastings, M. B. & Haah, J. Distillation with sublogarithmic overhead. Phys. Rev. Lett. 120, 050504 (2018).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Krishna, A. & Tillich, J.-P. Towards low overhead magic state distillation. Phys. Rev. Lett. 123, 070507 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Beverland, M., Campbell, E., Howard, M. & Kliuchnikov, V. Lower bounds on the non-clifford resources for quantum computations. Quantum Sci. Technol. 5, 035009 (2020).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jones, C. Low-overhead constructions for the fault-tolerant toffoli gate. Phys. Rev. A 87, 022328 (2013).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Selinger, P. Quantum circuits of t-depth one. Phys. Rev. A 87, 042302 (2013).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gidney, C. & Fowler, A. G. Efficient magic state factories with a catalyzed \\(\\left\\vert CCZ\\right\\rangle\\) to \\(\\left\\vert CCZ\\right\\rangle\\) transformation. Quantum 3, 135 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Goppa, V. D. Algebraico-geometric codes. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 46, 762 (1982).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gottesman, D. Surviving as a Quantum Computer in a Classical World (Self-Published, 2024).<\/p>\n

Vasmer, M. & Kubica, A. Morphing quantum codes. PRX Quantum 3, 030319 (2022).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Golowich, L. & Guruswami, V. Asymptotically good quantum codes with transversal non-Clifford gates. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2408.09254<\/a> (2024).<\/p>\n

Nguyen, Q. T., Good binary quantum codes with transversal ccz gate. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2408.10140<\/a> (2024).<\/p>\n

Calderbank, A. R. & Shor, P. W. Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098 (1996).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Steane, A. Multiple-particle interference and quantum error correction. Proc. R. Soc. London A 452, 2551 (1996).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

MacWilliams, F. J. & Sloane, N. J. A. The Theory of Error-Correcting Codes vol. 16 (Elsevier, 1977).<\/p>\n

Stichtenoth, H. Algebraic Function Fields and Codes vol. 254 (Springer, 2009).<\/p>\n

Houshmand, M., Zamani, M. S., Sedighi, M. & Arabzadeh, M. Decomposition of diagonal hermitian quantum gates using multiple-controlled pauli z gates. ACM J. Emerg. Technolog. Comput. Syst 11, 1 (2014).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Tsfasman, M. A., Vl\u0103dut, S. G., & Nogin, D. Algebraic Geometric Codes: Basic Notions vol. 139 (American Mathematical Society, 2007).<\/p>\n

Panteleev, P. & Kalachev, G. Asymptotically good quantum and locally testable classical LDPC codes. In Proc. 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 375\u2013388 (Association for Computing Machinery, 2022).<\/p>\n

Leverrier, A. and Zemor, G. Quantum tanner codes. In Proc. 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science 872\u2013883 (IEEE Computer Society, 2022).<\/p>\n

Dinur, I., Hsieh, M.-H., Lin, T.-C., and Vidick, T. Good quantum LDPC codes with linear time decoders. In Proc. 55th Annual ACM Symposium on Theory of Computing, STOC 2023 905\u2013918 (Association for Computing Machinery, 2023).<\/p>\n

Devetak, I. & Winter, A. Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A 461, 207 (2005).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bennett, C. H., Bernstein, H. J., Popescu, S. & Schumacher, B. Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Veitch, V., Ferrie, C., Gross, D. & Emerson, J. Negative quasi-probability as a resource for quantum computation. N. J. Phys. 14, 113011 (2012).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Veitch, V., Mousavian, S. A. H., Gottesman, D. & Emerson, J. The resource theory of stabilizer quantum computation. N. J. Phys. 16, 013009 (2014).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Howard, M. & Campbell, E. Application of a resource theory for magic states to fault-tolerant quantum computing. Phys. Rev. Lett. 118, 090501 (2017).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Hayashi, M. & Yamasaki, H. Generalized quantum Stein\u2019s lemma and second law of quantum resource theories. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2408.02722<\/a> (2024).<\/p>\n","protected":false},"excerpt":{"rendered":"Gottesman, D. An introduction to quantum error correction. Proc. Symp. Appl. Math. 58, 221\u2013236 (2002). Article\u00a0 MathSciNet\u00a0 Google…\n","protected":false},"author":2,"featured_media":26223,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[8005,8004,8008,2623,2298,2294,26390,8003,8006,111,139,69,8007,393,8756,147,8002],"class_list":{"0":"post-26222","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-atomic","9":"tag-classical-and-continuum-physics","10":"tag-complex-systems","11":"tag-computational-science","12":"tag-condensed-matter-physics","13":"tag-general","14":"tag-information-theory-and-computation","15":"tag-mathematical-and-computational-physics","16":"tag-molecular","17":"tag-new-zealand","18":"tag-newzealand","19":"tag-nz","20":"tag-optical-and-plasma-physics","21":"tag-physics","22":"tag-quantum-information","23":"tag-science","24":"tag-theoretical"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/posts\/26222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/comments?post=26222"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/posts\/26222\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/media\/26223"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/media?parent=26222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/categories?post=26222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/nz\/wp-json\/wp\/v2\/tags?post=26222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}