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arXiv · 2504.07497

Quantum Determinant Estimation

J. Agerskov·K. Splittorff
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Abstract

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.

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J. Agerskov, K. Splittorff. 2025-04-10. Quantum Determinant Estimation. https://arxiv.org/abs/2504.07497

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