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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.07497 |
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Table of 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.