  Quantum logic decomposition refers to decomposing a given quantum gate to a
set of physically implementable gates. An approach has been presented to
decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation
gates around z axis. In this paper, a special class of diagonal quantum gates,
namely diagonal Hermitian quantum gates, is considered and a new perspective to
the decomposition problem with respect to decomposing these gates is presented.
It is first shown that these gates can be decomposed to a set that solely
consists of multiple-controlled Z gates. Then a binary representation for the
diagonal Hermitian gates is introduced. It is shown that the binary
representations of multiple-controlled Z gates form a basis for the vector
space that is produced by the binary representations of all diagonal Hermitian
quantum gates. Moreover, the problem of decomposing a given diagonal Hermitian
gate is mapped to the problem of writing its binary representation in the
specific basis mentioned above. Moreover, CZ gate is suggested to be the
two-qubit gate in the decomposition library, instead of previously used CNOT
gate. Experimental results show that the proposed approach can lead to circuits
with lower costs in comparison with the previous ones.
