The power of noisy fermionic quantum computation
We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi (2006 Phys. Rev. A 73 042313) that under the assumption of perfect braiding operations, universal quantum computat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2013-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/15/1/013015 |
| _version_ | 1827874534544375808 |
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| author | Fernando de Melo Piotr Ćwikliński Barbara M Terhal |
| author_facet | Fernando de Melo Piotr Ćwikliński Barbara M Terhal |
| author_sort | Fernando de Melo |
| collection | DOAJ |
| description | We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi (2006 Phys. Rev. A 73 042313) that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular four-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in this region, while for noise rates below 53% we prove that the state is not a mixture of Gaussian states. These results are obtained by generalizing concepts in entanglement theory to the setting of Gaussian states and their convex mixtures. In particular, we develop a complete set of criteria, namely the existence of a Gaussian-symmetric extension, which determine whether a state is a convex mixture of Gaussian states. |
| first_indexed | 2024-03-12T16:53:18Z |
| format | Article |
| id | doaj.art-19525d7423af47ebace639c300fc50de |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:53:18Z |
| publishDate | 2013-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-19525d7423af47ebace639c300fc50de2023-08-08T11:03:05ZengIOP PublishingNew Journal of Physics1367-26302013-01-0115101301510.1088/1367-2630/15/1/013015The power of noisy fermionic quantum computationFernando de Melo0Piotr Ćwikliński1Barbara M Terhal2Centrum Wiskunde and Informatica, Science Park 123, 1098-XG Amsterdam, The NetherlandsInstitute for Quantum Information, RWTH Aachen University , D-52056 Aachen, GermanyInstitute for Quantum Information, RWTH Aachen University , D-52056 Aachen, GermanyWe consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi (2006 Phys. Rev. A 73 042313) that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular four-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in this region, while for noise rates below 53% we prove that the state is not a mixture of Gaussian states. These results are obtained by generalizing concepts in entanglement theory to the setting of Gaussian states and their convex mixtures. In particular, we develop a complete set of criteria, namely the existence of a Gaussian-symmetric extension, which determine whether a state is a convex mixture of Gaussian states.https://doi.org/10.1088/1367-2630/15/1/013015 |
| spellingShingle | Fernando de Melo Piotr Ćwikliński Barbara M Terhal The power of noisy fermionic quantum computation New Journal of Physics |
| title | The power of noisy fermionic quantum computation |
| title_full | The power of noisy fermionic quantum computation |
| title_fullStr | The power of noisy fermionic quantum computation |
| title_full_unstemmed | The power of noisy fermionic quantum computation |
| title_short | The power of noisy fermionic quantum computation |
| title_sort | power of noisy fermionic quantum computation |
| url | https://doi.org/10.1088/1367-2630/15/1/013015 |
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