Quantum Overlapping Tomography
It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of n qubits, one requires an exponential number of measurements in n, which is experimentally unfeasible even for mo...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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American Physical Society
2020
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| Online Access: | https://hdl.handle.net/1721.1/125495 |
| _version_ | 1811096516162486272 |
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| author | Cotler, Jordan Wilczek, Frank |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Cotler, Jordan Wilczek, Frank |
| author_sort | Cotler, Jordan |
| collection | MIT |
| description | It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of n qubits, one requires an exponential number of measurements in n, which is experimentally unfeasible even for modest system sizes. By leveraging (i) that single-qubit measurements can be made in parallel, and (ii) the theory of perfect hash families, we show that all k-qubit reduced density matrices of an n qubit state can be determined with at most e^{O(k)}log^{2}(n) rounds of parallel measurements. We provide concrete measurement protocols which realize this bound. As an example, we argue that with near-term experiments, every two-point correlator in a system of 1024 qubits could be measured and completely characterized in a few days. This corresponds to determining nearly 4.5 million correlators. Keywords: Quantum entanglement; Quantum tomography |
| first_indexed | 2024-09-23T16:44:55Z |
| format | Article |
| id | mit-1721.1/125495 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:44:55Z |
| publishDate | 2020 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1254952022-10-03T08:01:35Z Quantum Overlapping Tomography Cotler, Jordan Wilczek, Frank Massachusetts Institute of Technology. Center for Theoretical Physics It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of n qubits, one requires an exponential number of measurements in n, which is experimentally unfeasible even for modest system sizes. By leveraging (i) that single-qubit measurements can be made in parallel, and (ii) the theory of perfect hash families, we show that all k-qubit reduced density matrices of an n qubit state can be determined with at most e^{O(k)}log^{2}(n) rounds of parallel measurements. We provide concrete measurement protocols which realize this bound. As an example, we argue that with near-term experiments, every two-point correlator in a system of 1024 qubits could be measured and completely characterized in a few days. This corresponds to determining nearly 4.5 million correlators. Keywords: Quantum entanglement; Quantum tomography U.S. Department of Energy (Grant DE-SC0012567) European Research Council (Grant 742104) Swedish Research Council (Grant 335-2014-7424) 2020-05-27T14:09:52Z 2020-05-27T14:09:52Z 2020-03 2019-08 2020-03-10T16:52:27Z Article http://purl.org/eprint/type/JournalArticle 1079-7114 0031-9007 https://hdl.handle.net/1721.1/125495 Cotler, Jordan and Wilczek, Frank, "Quantum Overlapping Tomography" Physical Review Letters 124 (March 2020): 100401 © 2020 American Physical Society en https://dx.doi.org/10.1103/PhysRevLett.124.100401 Physical Review Letters 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 | Cotler, Jordan Wilczek, Frank Quantum Overlapping Tomography |
| title | Quantum Overlapping Tomography |
| title_full | Quantum Overlapping Tomography |
| title_fullStr | Quantum Overlapping Tomography |
| title_full_unstemmed | Quantum Overlapping Tomography |
| title_short | Quantum Overlapping Tomography |
| title_sort | quantum overlapping tomography |
| url | https://hdl.handle.net/1721.1/125495 |
| work_keys_str_mv | AT cotlerjordan quantumoverlappingtomography AT wilczekfrank quantumoverlappingtomography |