Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely diffic...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/8/085011 |
| _version_ | 1797751297310457856 |
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| author | Tommaso F Demarie Trond Linjordet Nicolas C Menicucci Gavin K Brennen |
| author_facet | Tommaso F Demarie Trond Linjordet Nicolas C Menicucci Gavin K Brennen |
| author_sort | Tommaso F Demarie |
| collection | DOAJ |
| description | The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology. |
| first_indexed | 2024-03-12T16:47:24Z |
| format | Article |
| id | doaj.art-3e43a4a978c64f3bb196dea3a4673d95 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:47:24Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-3e43a4a978c64f3bb196dea3a4673d952023-08-08T11:31:00ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116808501110.1088/1367-2630/16/8/085011Detecting topological entanglement entropy in a lattice of quantum harmonic oscillatorsTommaso F Demarie0Trond Linjordet1Nicolas C Menicucci2Gavin K Brennen3Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University , North Ryde, NSW 2109, Australia; Singapore University of Technology and Design , 20 Dover Drive, 138682 Singapore, SingaporeCentre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University , North Ryde, NSW 2109, AustraliaSchool of Physics, The University of Sydney , Sydney, NSW 2006, AustraliaCentre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University , North Ryde, NSW 2109, AustraliaThe Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology.https://doi.org/10.1088/1367-2630/16/8/085011topological quantum computationcontinuous-variable quantum informationGaussian states |
| spellingShingle | Tommaso F Demarie Trond Linjordet Nicolas C Menicucci Gavin K Brennen Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators New Journal of Physics topological quantum computation continuous-variable quantum information Gaussian states |
| title | Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators |
| title_full | Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators |
| title_fullStr | Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators |
| title_full_unstemmed | Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators |
| title_short | Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators |
| title_sort | detecting topological entanglement entropy in a lattice of quantum harmonic oscillators |
| topic | topological quantum computation continuous-variable quantum information Gaussian states |
| url | https://doi.org/10.1088/1367-2630/16/8/085011 |
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