Computational speed-up with a single qudit
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical...
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| Format: | Online |
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Nature Publishing Group
2015
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4597186/ |
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pubmed-45971862015-10-13 Computational speed-up with a single qudit Gedik, Z. Silva, I. A. Çakmak, B. Karpat, G. Vidoto, E. L. G. Soares-Pinto, D. O. deAzevedo, E. R. Fanchini, F. F. Article Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart. Nature Publishing Group 2015-10-08 /pmc/articles/PMC4597186/ /pubmed/26446614 http://dx.doi.org/10.1038/srep14671 Text en Copyright © 2015, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
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Open Access Journal |
| institution_category |
Foreign Institution |
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US National Center for Biotechnology Information |
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NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Gedik, Z. Silva, I. A. Çakmak, B. Karpat, G. Vidoto, E. L. G. Soares-Pinto, D. O. deAzevedo, E. R. Fanchini, F. F. |
| spellingShingle |
Gedik, Z. Silva, I. A. Çakmak, B. Karpat, G. Vidoto, E. L. G. Soares-Pinto, D. O. deAzevedo, E. R. Fanchini, F. F. Computational speed-up with a single qudit |
| author_facet |
Gedik, Z. Silva, I. A. Çakmak, B. Karpat, G. Vidoto, E. L. G. Soares-Pinto, D. O. deAzevedo, E. R. Fanchini, F. F. |
| author_sort |
Gedik, Z. |
| title |
Computational speed-up with a single qudit |
| title_short |
Computational speed-up with a single qudit |
| title_full |
Computational speed-up with a single qudit |
| title_fullStr |
Computational speed-up with a single qudit |
| title_full_unstemmed |
Computational speed-up with a single qudit |
| title_sort |
computational speed-up with a single qudit |
| description |
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart. |
| publisher |
Nature Publishing Group |
| publishDate |
2015 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4597186/ |
| _version_ |
1613484867330244608 |