Decomposition of Diagonal Hermitian Quantum Gates Using Multiple-Controlled Pauli Z Gates

TL;DR

This paper introduces a novel method for decomposing diagonal Hermitian quantum gates into multiple-controlled Z gates, utilizing binary representations and a new basis, resulting in more cost-effective quantum circuits.

Contribution

It presents a new decomposition approach for diagonal Hermitian gates using multiple-controlled Z gates and a binary basis, replacing CNOT with CZ gates for improved efficiency.

Findings

Decomposition reduces circuit cost compared to previous methods.

Binary basis effectively represents diagonal Hermitian gates.

Replacing CNOT with CZ gates improves circuit efficiency.

Abstract

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.