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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.05468 |
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| _version_ | 1866913145330597888 |
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| author | Rodríguez, John A. Mora Dutra, Arthur C. R. Earp, Henrique N. Sá Cunha, Marcelo Terra |
| author_facet | Rodríguez, John A. Mora Dutra, Arthur C. R. Earp, Henrique N. Sá Cunha, Marcelo Terra |
| contents | We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by Sá Earp and Pachos (2005), we overcome key limitations of their method, such as reliance on ill-defined matrix logarithms and the convergence issues of truncated Baker-Campbell-Hausdorff(BCH) series. Our reformulation leverages the algebraic structure of involutive automorphisms and symmetric Lie algebra decompositions to yield a stable and recursive factorization process. We provide a full Python implementation of the algorithm, available in an open-source repository, and validate its performance on matrices in $SU(8)$ and $SU(16)$ using random unitary benchmarks. The algorithm produces decompositions that are directly suited to practical quantum hardware, with factors that can be implemented near-optimally using standard gate sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartan-Khaneja-Glaser decomposition of $SU(2^n)$ via involutive automorphisms Rodríguez, John A. Mora Dutra, Arthur C. R. Earp, Henrique N. Sá Cunha, Marcelo Terra Quantum Physics We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by Sá Earp and Pachos (2005), we overcome key limitations of their method, such as reliance on ill-defined matrix logarithms and the convergence issues of truncated Baker-Campbell-Hausdorff(BCH) series. Our reformulation leverages the algebraic structure of involutive automorphisms and symmetric Lie algebra decompositions to yield a stable and recursive factorization process. We provide a full Python implementation of the algorithm, available in an open-source repository, and validate its performance on matrices in $SU(8)$ and $SU(16)$ using random unitary benchmarks. The algorithm produces decompositions that are directly suited to practical quantum hardware, with factors that can be implemented near-optimally using standard gate sets. |
| title | Cartan-Khaneja-Glaser decomposition of $SU(2^n)$ via involutive automorphisms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.05468 |