Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation
All known resource states for measurement-based quantum teleportation in correlation space possess symmetry-protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013134 |
| _version_ | 1797210239127257088 |
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| author | Zhuohao Liu Emma C. Johnson David L. Feder |
| author_facet | Zhuohao Liu Emma C. Johnson David L. Feder |
| author_sort | Zhuohao Liu |
| collection | DOAJ |
| description | All known resource states for measurement-based quantum teleportation in correlation space possess symmetry-protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-on-site symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry. |
| first_indexed | 2024-04-24T10:07:26Z |
| format | Article |
| id | doaj.art-76fd9cacd1da4f00a235c6af5bd83a07 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:26Z |
| publishDate | 2024-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-76fd9cacd1da4f00a235c6af5bd83a072024-04-12T17:38:50ZengAmerican Physical SocietyPhysical Review Research2643-15642024-02-016101313410.1103/PhysRevResearch.6.013134Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportationZhuohao LiuEmma C. JohnsonDavid L. FederAll known resource states for measurement-based quantum teleportation in correlation space possess symmetry-protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-on-site symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry.http://doi.org/10.1103/PhysRevResearch.6.013134 |
| spellingShingle | Zhuohao Liu Emma C. Johnson David L. Feder Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation Physical Review Research |
| title | Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation |
| title_full | Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation |
| title_fullStr | Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation |
| title_full_unstemmed | Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation |
| title_short | Symmetry-protected topological order as a requirement for measurement-based quantum gate teleportation |
| title_sort | symmetry protected topological order as a requirement for measurement based quantum gate teleportation |
| url | http://doi.org/10.1103/PhysRevResearch.6.013134 |
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