Determining system Hamiltonian from eigenstate measurements without correlation functions
Local Hamiltonians arise naturally in physical systems. Despite their seemingly ‘simple’ local structures, exotic features such as non-local correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenst...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/abaacf |
| _version_ | 1797750396825894912 |
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| author | Shi-Yao Hou Ningping Cao Sirui Lu Yi Shen Yiu-Tung Poon Bei Zeng |
| author_facet | Shi-Yao Hou Ningping Cao Sirui Lu Yi Shen Yiu-Tung Poon Bei Zeng |
| author_sort | Shi-Yao Hou |
| collection | DOAJ |
| description | Local Hamiltonians arise naturally in physical systems. Despite their seemingly ‘simple’ local structures, exotic features such as non-local correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate $\left\vert \psi \right\rangle $ require information of nonlocal correlation functions. In this work, we argue that local measurements on $\left\vert \psi \right\rangle $ is enough to recover the Hamiltonian in most of the cases. Specially, we develop an algorithm to demonstrate the observation. Our algorithm is tested numerically for randomly generated local Hamiltonians of different system sizes and returns promising reconstructions with desired accuracy. Additionally, for random generated Hamiltonians (not necessarily local), our algorithm also provides precise estimations. |
| first_indexed | 2024-03-12T16:32:10Z |
| format | Article |
| id | doaj.art-23edd0e0f8564328889e6383e9f94eb0 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:32:10Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-23edd0e0f8564328889e6383e9f94eb02023-08-08T15:24:37ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122808308810.1088/1367-2630/abaacfDetermining system Hamiltonian from eigenstate measurements without correlation functionsShi-Yao Hou0https://orcid.org/0000-0001-9739-2263Ningping Cao1Sirui Lu2Yi Shen3Yiu-Tung Poon4Bei Zeng5College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University , Chengdu 610068, People’s Republic of China; Department of Physics, The Hong Kong University of Science and Technology , Clear Water Bay, Kowloon, Hong Kong, People’s Republic of ChinaDepartment of Mathematics & Statistics, University of Guelph , Guelph N1G 2W1, Ontario, Canada; Institute for Quantum Computing, University of Waterloo , Waterloo N2L 3G1, Ontario, CanadaMax-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, GermanyDepartment of Statistics and Actuarial Science, University of Waterloo , Waterloo, Ontario, CanadaDepartment of Mathematics, Iowa State University , Ames, Iowa, IA 50011, United States of AmericaDepartment of Physics, The Hong Kong University of Science and Technology , Clear Water Bay, Kowloon, Hong Kong, People’s Republic of ChinaLocal Hamiltonians arise naturally in physical systems. Despite their seemingly ‘simple’ local structures, exotic features such as non-local correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate $\left\vert \psi \right\rangle $ require information of nonlocal correlation functions. In this work, we argue that local measurements on $\left\vert \psi \right\rangle $ is enough to recover the Hamiltonian in most of the cases. Specially, we develop an algorithm to demonstrate the observation. Our algorithm is tested numerically for randomly generated local Hamiltonians of different system sizes and returns promising reconstructions with desired accuracy. Additionally, for random generated Hamiltonians (not necessarily local), our algorithm also provides precise estimations.https://doi.org/10.1088/1367-2630/abaacfeigenstateHamiltonian determinationgradient based optimization methodno correlation functions |
| spellingShingle | Shi-Yao Hou Ningping Cao Sirui Lu Yi Shen Yiu-Tung Poon Bei Zeng Determining system Hamiltonian from eigenstate measurements without correlation functions New Journal of Physics eigenstate Hamiltonian determination gradient based optimization method no correlation functions |
| title | Determining system Hamiltonian from eigenstate measurements without correlation functions |
| title_full | Determining system Hamiltonian from eigenstate measurements without correlation functions |
| title_fullStr | Determining system Hamiltonian from eigenstate measurements without correlation functions |
| title_full_unstemmed | Determining system Hamiltonian from eigenstate measurements without correlation functions |
| title_short | Determining system Hamiltonian from eigenstate measurements without correlation functions |
| title_sort | determining system hamiltonian from eigenstate measurements without correlation functions |
| topic | eigenstate Hamiltonian determination gradient based optimization method no correlation functions |
| url | https://doi.org/10.1088/1367-2630/abaacf |
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