The resource theory of stabilizer quantum computation
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for fault-tolerant s...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/16/1/013009 |
| _version_ | 1827874274937929728 |
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| author | Victor Veitch S A Hamed Mousavian Daniel Gottesman Joseph Emerson |
| author_facet | Victor Veitch S A Hamed Mousavian Daniel Gottesman Joseph Emerson |
| author_sort | Victor Veitch |
| collection | DOAJ |
| description | Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for fault-tolerant stabilizer computation. We introduce two quantitative measures—monotones—for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behavior. |
| first_indexed | 2024-03-12T16:49:55Z |
| format | Article |
| id | doaj.art-c34e7f9202f94a5da64e8b17069ee564 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:49:55Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-c34e7f9202f94a5da64e8b17069ee5642023-08-08T11:25:16ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116101300910.1088/1367-2630/16/1/013009The resource theory of stabilizer quantum computationVictor Veitch0S A Hamed Mousavian1Daniel Gottesman2Joseph Emerson3Institute for Quantum Computing, University of Waterloo , Waterloo, N2L 3G1 ON, Canada; Department of Applied Mathematics, University of Waterloo , Waterloo, N2L 3G1 ON, CanadaPerimeter Institute for Theoretical Physics , Waterloo, N2L 2Y5 ON, CanadaPerimeter Institute for Theoretical Physics , Waterloo, N2L 2Y5 ON, CanadaInstitute for Quantum Computing, University of Waterloo , Waterloo, N2L 3G1 ON, Canada; Department of Applied Mathematics, University of Waterloo , Waterloo, N2L 3G1 ON, CanadaRecent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for fault-tolerant stabilizer computation. We introduce two quantitative measures—monotones—for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behavior.https://doi.org/10.1088/1367-2630/16/1/013009 |
| spellingShingle | Victor Veitch S A Hamed Mousavian Daniel Gottesman Joseph Emerson The resource theory of stabilizer quantum computation New Journal of Physics |
| title | The resource theory of stabilizer quantum computation |
| title_full | The resource theory of stabilizer quantum computation |
| title_fullStr | The resource theory of stabilizer quantum computation |
| title_full_unstemmed | The resource theory of stabilizer quantum computation |
| title_short | The resource theory of stabilizer quantum computation |
| title_sort | resource theory of stabilizer quantum computation |
| url | https://doi.org/10.1088/1367-2630/16/1/013009 |
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