Resources required for topological quantum factoring
We consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1797092975507931136 |
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| author | Baraban, M Bonesteel, N Simon, S |
| author_facet | Baraban, M Bonesteel, N Simon, S |
| author_sort | Baraban, M |
| collection | OXFORD |
| description | We consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method which combines topological and nontopological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128-bit number requires approximately 103 Fibonacci anyons versus at least 3×109 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially. © 2010 The American Physical Society. |
| first_indexed | 2024-03-07T03:53:42Z |
| format | Journal article |
| id | oxford-uuid:c2239406-4489-4e8a-be62-b1c5cf264048 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:53:42Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:c2239406-4489-4e8a-be62-b1c5cf2640482022-03-27T06:06:44ZResources required for topological quantum factoringJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c2239406-4489-4e8a-be62-b1c5cf264048EnglishSymplectic Elements at Oxford2010Baraban, MBonesteel, NSimon, SWe consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method which combines topological and nontopological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128-bit number requires approximately 103 Fibonacci anyons versus at least 3×109 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially. © 2010 The American Physical Society. |
| spellingShingle | Baraban, M Bonesteel, N Simon, S Resources required for topological quantum factoring |
| title | Resources required for topological quantum factoring |
| title_full | Resources required for topological quantum factoring |
| title_fullStr | Resources required for topological quantum factoring |
| title_full_unstemmed | Resources required for topological quantum factoring |
| title_short | Resources required for topological quantum factoring |
| title_sort | resources required for topological quantum factoring |
| work_keys_str_mv | AT barabanm resourcesrequiredfortopologicalquantumfactoring AT bonesteeln resourcesrequiredfortopologicalquantumfactoring AT simons resourcesrequiredfortopologicalquantumfactoring |