Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911089141219328 |
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| author | Lootens, Laurens Delcamp, Clement Williamson, Dominic Verstraete, Frank |
| author_facet | Lootens, Laurens Delcamp, Clement Williamson, Dominic Verstraete, Frank |
| contents | A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine closed boundary conditions and charge sectors, these can be implemented by unitary matrix product operators. In this manuscript, we explain how to turn such duality operators into unitary linear depth quantum circuits via the introduction of ancillary degrees of freedom that keep track of the various sectors. The linear depth is consistent with the fact that these dualities change the phase of the states on which they act. When supplemented with measurements, we show that dualities with respect to symmetries encoded into nilpotent fusion categories can be realised in constant depth. The resulting circuits can for instance be used to efficiently prepare short- and long-range entangled states or map between different gapped boundaries of (2+1)d topological models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01439 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models Lootens, Laurens Delcamp, Clement Williamson, Dominic Verstraete, Frank Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine closed boundary conditions and charge sectors, these can be implemented by unitary matrix product operators. In this manuscript, we explain how to turn such duality operators into unitary linear depth quantum circuits via the introduction of ancillary degrees of freedom that keep track of the various sectors. The linear depth is consistent with the fact that these dualities change the phase of the states on which they act. When supplemented with measurements, we show that dualities with respect to symmetries encoded into nilpotent fusion categories can be realised in constant depth. The resulting circuits can for instance be used to efficiently prepare short- and long-range entangled states or map between different gapped boundaries of (2+1)d topological models. |
| title | Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2311.01439 |