Quantum-Logic Synthesis of Hermitian Gates

TL;DR

This paper introduces a novel quantum circuit synthesis method for Hermitian gates based on an extended Jacobi approach, enabling efficient implementation with linear gate complexity and auxiliary qubits.

Contribution

It presents a new synthesis technique for Hermitian quantum gates using an extended Jacobi method, optimizing gate implementation and complexity.

Findings

Efficient synthesis of Hermitian gates with linear gate count.

Implementation of multiple-control gates using auxiliary qubits.

Reduction of complex Hermitian gates to elementary quantum gates.

Abstract

In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in linear algebra is considered as the basis of the proposed synthesis method. The quantum circuit synthesis method derived from the Jacobi approach and its optimization challenges are described. It is shown that the proposed method results in multiple-control rotation gates around the y axis, multiple-control phase shift gates, multiple-control NOT gates and a middle diagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Z gates. 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 a linear number of elementary gates in terms of circuit lines with the aid of one auxiliary qubit in an arbitrary state.