Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quant...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114260 https://orcid.org/0000-0003-3539-6140 https://orcid.org/0000-0003-3207-594X |
| _version_ | 1826194360440455168 |
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| author | Sone, Akira Cappellaro, Paola |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Sone, Akira Cappellaro, Paola |
| author_sort | Sone, Akira |
| collection | MIT |
| description | Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved. |
| first_indexed | 2024-09-23T09:54:29Z |
| format | Article |
| id | mit-1721.1/114260 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:54:29Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1142602022-09-26T14:31:54Z Exact dimension estimation of interacting qubit systems assisted by a single quantum probe Sone, Akira Cappellaro, Paola Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Sone, Akira Cappellaro, Paola Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved. National Science Foundation (U.S.) (PHY0551153) United States. Army Research Office (Grant W911NF-15-1-0548) United States. Army Research Office (Grant W911NF-11-1-0400) 2018-03-23T17:03:00Z 2018-03-23T17:03:00Z 2017-12 2018-02-07T20:55:42Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 http://hdl.handle.net/1721.1/114260 Sone, Akira, and Paola Cappellaro. “Exact Dimension Estimation of Interacting Qubit Systems Assisted by a Single Quantum Probe.” Physical Review A, vol. 96, no. 6, Dec. 2017. © 2017 American Physical Society https://orcid.org/0000-0003-3539-6140 https://orcid.org/0000-0003-3207-594X en http://dx.doi.org/10.1103/PhysRevA.96.062334 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Sone, Akira Cappellaro, Paola Exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| title | Exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| title_full | Exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| title_fullStr | Exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| title_full_unstemmed | Exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| title_short | Exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| title_sort | exact dimension estimation of interacting qubit systems assisted by a single quantum probe |
| url | http://hdl.handle.net/1721.1/114260 https://orcid.org/0000-0003-3539-6140 https://orcid.org/0000-0003-3207-594X |
| work_keys_str_mv | AT soneakira exactdimensionestimationofinteractingqubitsystemsassistedbyasinglequantumprobe AT cappellaropaola exactdimensionestimationofinteractingqubitsystemsassistedbyasinglequantumprobe |