Polynomial-depth quantum algorithm for computing matrix determinant
arxiv(2024)
摘要
We propose an algorithm for calculating the determinant of a square matrix,
and construct the quantum circuit realizing it, using multiqubit control gates
(representable in terms of Toffoli gates, CNOTs and SWAPs), Hadamard
transformations and Z-operators. Each row of the matrix is encoded as a pure
state of some quantum system. The admitted matrix is therefore arbitrary up to
the normalization of quantum states of those systems. The depth of the proposed
algorithm is O(N^3log N) for the N× N matrix.
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