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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2405.09361 |
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| _version_ | 1866910458539147264 |
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| author | Khan, Maaz Khan, Syed Anausha Bin Zakir Mohd, Arif |
| author_facet | Khan, Maaz Khan, Syed Anausha Bin Zakir Mohd, Arif |
| contents | We study the Kramers-Wannier duality for the transverse-field Ising lattice on a ring. A careful consideration of the ring boundary conditions shows that the duality has to be implemented with a proper treatment of different charge sectors of both the twisted and untwisted Ising and the dual-Ising Hilbert spaces. We construct a superoperator that explicitly maps the Ising operators to the dual-Ising operators. The superoperator naturally acts on the tensor product of the Ising and the dual-Ising Hilbert space. We then show that the relation between our superoperator and the Kramers-Wannier duality operator that maps the Ising Hilbert space to the dual-Ising Hilbert space is naturally provided by quantum operations and the duality can be understood as a quantum operation that we construct. We provide the operator-sum representation for the Kramers-Wannier quantum operations and reproduce the well-known fusion rules. In addition to providing the quantum information perspective on the Kramers-Wannier duality, our explicit protocol will also be useful in implementing the Kramers-Wannier duality on a quantum computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum operations for Kramers-Wannier duality Khan, Maaz Khan, Syed Anausha Bin Zakir Mohd, Arif High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics We study the Kramers-Wannier duality for the transverse-field Ising lattice on a ring. A careful consideration of the ring boundary conditions shows that the duality has to be implemented with a proper treatment of different charge sectors of both the twisted and untwisted Ising and the dual-Ising Hilbert spaces. We construct a superoperator that explicitly maps the Ising operators to the dual-Ising operators. The superoperator naturally acts on the tensor product of the Ising and the dual-Ising Hilbert space. We then show that the relation between our superoperator and the Kramers-Wannier duality operator that maps the Ising Hilbert space to the dual-Ising Hilbert space is naturally provided by quantum operations and the duality can be understood as a quantum operation that we construct. We provide the operator-sum representation for the Kramers-Wannier quantum operations and reproduce the well-known fusion rules. In addition to providing the quantum information perspective on the Kramers-Wannier duality, our explicit protocol will also be useful in implementing the Kramers-Wannier duality on a quantum computer. |
| title | Quantum operations for Kramers-Wannier duality |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2405.09361 |