Quantum Determinant Estimation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918060996165632 |
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| author | Agerskov, J. Splittorff, K. |
| author_facet | Agerskov, J. Splittorff, K. |
| contents | A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with $\mathcal{O}(N\log^2 N+t^2)$ operations and $tN$ controlled applications of $U^{2^m}$ with $m=0,\ldots,t-1$. For an orthogonal matrix $O\in O(N)$ the algorithm can determine with certainty the sign of the determinant using $\mathcal{O}(N\log^2 N)$ operations and $N$ controlled applications of $O$. An extension of the algorithm to contractions is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Determinant Estimation Agerskov, J. Splittorff, K. Quantum Physics High Energy Physics - Lattice A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with $\mathcal{O}(N\log^2 N+t^2)$ operations and $tN$ controlled applications of $U^{2^m}$ with $m=0,\ldots,t-1$. For an orthogonal matrix $O\in O(N)$ the algorithm can determine with certainty the sign of the determinant using $\mathcal{O}(N\log^2 N)$ operations and $N$ controlled applications of $O$. An extension of the algorithm to contractions is discussed. |
| title | Quantum Determinant Estimation |
| topic | Quantum Physics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2504.07497 |