An Extension of Gauss-Bonnet's Theorem D: Gauss-Bonnet Theorem under Braid Group Representations and Its Applications in Topological Quantum Computation
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2025
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| _version_ | 1866901605735989248 |
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>This paper studies the categorification extension of the Gauss-Bonnet theorem<br> within the framework of braid group representations. By introducing the concept<br> of quantum curvature and topological invariants based on braid group representa<br>tions, we establish a generalized Gauss-Bonnet formula applicable to surfaces with<br> anyon excitations. This formula generalizes the Euler characteristic in the classi<br>cal theorem to a quantum Euler characteristic and establishes a direct connection<br> with the number of logical qubits in topological quantum computation through<br> the quantum dimension. The theoretical framework is mathematically rigorous<br> and self-consistent, and physically provides a new geometric description tool for<br> topological quantum computation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17423322 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | An Extension of Gauss-Bonnet's Theorem D: Gauss-Bonnet Theorem under Braid Group Representations and Its Applications in Topological Quantum Computation zhou, changzheng zhou, ziqing Gauss-Bonnet Theorem; Braid Group Representations; Quantum Cur vature; Anyon Statistics; Topological Quantum Computation; Categorification; Quantum Dimension; Quantum Euler Characteristic <p>This paper studies the categorification extension of the Gauss-Bonnet theorem<br> within the framework of braid group representations. By introducing the concept<br> of quantum curvature and topological invariants based on braid group representa<br>tions, we establish a generalized Gauss-Bonnet formula applicable to surfaces with<br> anyon excitations. This formula generalizes the Euler characteristic in the classi<br>cal theorem to a quantum Euler characteristic and establishes a direct connection<br> with the number of logical qubits in topological quantum computation through<br> the quantum dimension. The theoretical framework is mathematically rigorous<br> and self-consistent, and physically provides a new geometric description tool for<br> topological quantum computation.</p> |
| title | An Extension of Gauss-Bonnet's Theorem D: Gauss-Bonnet Theorem under Braid Group Representations and Its Applications in Topological Quantum Computation |
| topic | Gauss-Bonnet Theorem; Braid Group Representations; Quantum Cur vature; Anyon Statistics; Topological Quantum Computation; Categorification; Quantum Dimension; Quantum Euler Characteristic |
| url | https://doi.org/10.5281/zenodo.17423322 |