Quantum Algorithms: Entanglement Enhanced Information Processing
We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We d...
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| Format: | Journal article |
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1998
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| _version_ | 1826288198368624640 |
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| author | Ekert, A Jozsa, R |
| author_facet | Ekert, A Jozsa, R |
| author_sort | Ekert, A |
| collection | OXFORD |
| description | We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms. |
| first_indexed | 2024-03-07T02:10:05Z |
| format | Journal article |
| id | oxford-uuid:a05409a6-0e8b-4e67-bcdd-73085d3d3bf4 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:10:05Z |
| publishDate | 1998 |
| record_format | dspace |
| spelling | oxford-uuid:a05409a6-0e8b-4e67-bcdd-73085d3d3bf42022-03-27T02:04:36ZQuantum Algorithms: Entanglement Enhanced Information ProcessingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a05409a6-0e8b-4e67-bcdd-73085d3d3bf4Symplectic Elements at Oxford1998Ekert, AJozsa, RWe discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms. |
| spellingShingle | Ekert, A Jozsa, R Quantum Algorithms: Entanglement Enhanced Information Processing |
| title | Quantum Algorithms: Entanglement Enhanced Information Processing |
| title_full | Quantum Algorithms: Entanglement Enhanced Information Processing |
| title_fullStr | Quantum Algorithms: Entanglement Enhanced Information Processing |
| title_full_unstemmed | Quantum Algorithms: Entanglement Enhanced Information Processing |
| title_short | Quantum Algorithms: Entanglement Enhanced Information Processing |
| title_sort | quantum algorithms entanglement enhanced information processing |
| work_keys_str_mv | AT ekerta quantumalgorithmsentanglementenhancedinformationprocessing AT jozsar quantumalgorithmsentanglementenhancedinformationprocessing |