In this paper, the problem of synthesizing a general Hermitian quantum gateinto a set of primary quantum gates is addressed. To this end, an extendedversion of the Jacobi approach for calculating the eigenvalues of Hermitianmatrices in linear algebra is considered as the basis of the proposed synthesismethod. The quantum circuit synthesis method derived from the Jacobi approachand its optimization challenges are described. It is shown that the proposedmethod results in multiple-control rotation gates around the y axis,multiple-control phase shift gates, multiple-control NOT gates and a middlediagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Zgates. Using the proposed approach, it is shown how multiple-control U gates,where U is a single-qubit Hermitian quantum gate, can be implemented using alinear number of elementary gates in terms of circuit lines with the aid of oneauxiliary qubit in an arbitrary state.
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