Characterizing MPS and PEPS Preparable via Measurement and Feedback
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914987619909632 |
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| author | Zhang, Yifan Gopalakrishnan, Sarang Styliaris, Georgios |
| author_facet | Zhang, Yifan Gopalakrishnan, Sarang Styliaris, Georgios |
| contents | Preparing long-range entangled states poses significant challenges for near-term quantum devices. It is known that measurement and feedback (MF) can aid this task by allowing the preparation of certain paradigmatic long-range entangled states with only constant circuit depth. Here we systematically explore the structure of states that can be prepared using constant-depth local circuits and a single MF round. Using the framework of tensor networks, the preparability under MF translates to tensor symmetries. We detail the structure of matrix-product states (MPS) and projected entangled-pair states (PEPS) that can be prepared using MF, revealing the coexistence of Clifford-like properties and magic. In one dimension, we show that states with abelian symmetry protected topological order are a restricted class of MF-preparable states. In two dimensions, we parameterize a subset of states with abelian topological order that are MF-preparable. Finally, we discuss the analogous implementation of operators via MF, providing a structural theorem that connects to the well-known Clifford teleportation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing MPS and PEPS Preparable via Measurement and Feedback Zhang, Yifan Gopalakrishnan, Sarang Styliaris, Georgios Quantum Physics Strongly Correlated Electrons Preparing long-range entangled states poses significant challenges for near-term quantum devices. It is known that measurement and feedback (MF) can aid this task by allowing the preparation of certain paradigmatic long-range entangled states with only constant circuit depth. Here we systematically explore the structure of states that can be prepared using constant-depth local circuits and a single MF round. Using the framework of tensor networks, the preparability under MF translates to tensor symmetries. We detail the structure of matrix-product states (MPS) and projected entangled-pair states (PEPS) that can be prepared using MF, revealing the coexistence of Clifford-like properties and magic. In one dimension, we show that states with abelian symmetry protected topological order are a restricted class of MF-preparable states. In two dimensions, we parameterize a subset of states with abelian topological order that are MF-preparable. Finally, we discuss the analogous implementation of operators via MF, providing a structural theorem that connects to the well-known Clifford teleportation. |
| title | Characterizing MPS and PEPS Preparable via Measurement and Feedback |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2405.09615 |