Topological sum rule for geometric phases of quantum gates
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913175459332096 |
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| author | Orion, Nadav Rotstein, Boris Miller, Nirron Akkermans, Eric |
| author_facet | Orion, Nadav Rotstein, Boris Miller, Nirron Akkermans, Eric |
| contents | We establish a topological sum rule, $ν_U = \frac{1}{2π}\sum_nγ_n = mν_H$, connecting the geometric phases accumulated by a two-qubit system over a complete basis of initial states to the winding number $ν_H$ classifying its Hamiltonian. Implementations of the same gate from different topological classes must distribute these phases differently, making their distinction measurable through the Wootters concurrence. As a corollary, nontrivial topology is a necessary condition for entanglement: only Hamiltonians with access to $ν_H \neq 0$ can generate it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological sum rule for geometric phases of quantum gates Orion, Nadav Rotstein, Boris Miller, Nirron Akkermans, Eric Quantum Physics We establish a topological sum rule, $ν_U = \frac{1}{2π}\sum_nγ_n = mν_H$, connecting the geometric phases accumulated by a two-qubit system over a complete basis of initial states to the winding number $ν_H$ classifying its Hamiltonian. Implementations of the same gate from different topological classes must distribute these phases differently, making their distinction measurable through the Wootters concurrence. As a corollary, nontrivial topology is a necessary condition for entanglement: only Hamiltonians with access to $ν_H \neq 0$ can generate it. |
| title | Topological sum rule for geometric phases of quantum gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.29795 |