Statistical approach to quantum phase estimation
We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate–eigenphase pair from a given unitary matrix utilizing a simpli...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2021-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ac320d |
| _version_ | 1797749966254374912 |
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| author | Alexandria J Moore Yuchen Wang Zixuan Hu Sabre Kais Andrew M Weiner |
| author_facet | Alexandria J Moore Yuchen Wang Zixuan Hu Sabre Kais Andrew M Weiner |
| author_sort | Alexandria J Moore |
| collection | DOAJ |
| description | We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate–eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate–eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate–eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer. |
| first_indexed | 2024-03-12T16:27:10Z |
| format | Article |
| id | doaj.art-1b976942b12d40f7aa29f8b323568831 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:10Z |
| publishDate | 2021-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-1b976942b12d40f7aa29f8b3235688312023-08-08T15:40:41ZengIOP PublishingNew Journal of Physics1367-26302021-01-01231111302710.1088/1367-2630/ac320dStatistical approach to quantum phase estimationAlexandria J Moore0https://orcid.org/0000-0001-7385-4435Yuchen Wang1Zixuan Hu2Sabre Kais3https://orcid.org/0000-0003-0574-5346Andrew M Weiner4School of Electrical and Computer Engineering and Purdue Quantum Science and Engineering Institute, Purdue University , West Lafayette, IN 47907, United States of AmericaDepartment of Chemistry, Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University , West Lafayette, IN 47907, United States of AmericaDepartment of Chemistry, Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University , West Lafayette, IN 47907, United States of AmericaDepartment of Chemistry, Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University , West Lafayette, IN 47907, United States of AmericaSchool of Electrical and Computer Engineering and Purdue Quantum Science and Engineering Institute, Purdue University , West Lafayette, IN 47907, United States of AmericaWe introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate–eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate–eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate–eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer.https://doi.org/10.1088/1367-2630/ac320dquantum computationquantum informationquantum algorithmsquantum chemistry |
| spellingShingle | Alexandria J Moore Yuchen Wang Zixuan Hu Sabre Kais Andrew M Weiner Statistical approach to quantum phase estimation New Journal of Physics quantum computation quantum information quantum algorithms quantum chemistry |
| title | Statistical approach to quantum phase estimation |
| title_full | Statistical approach to quantum phase estimation |
| title_fullStr | Statistical approach to quantum phase estimation |
| title_full_unstemmed | Statistical approach to quantum phase estimation |
| title_short | Statistical approach to quantum phase estimation |
| title_sort | statistical approach to quantum phase estimation |
| topic | quantum computation quantum information quantum algorithms quantum chemistry |
| url | https://doi.org/10.1088/1367-2630/ac320d |
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