Quantum-Logic Synthesis of Hermitian 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.

Optimizing Teleportation Cost in Distributed Quantum Circuits

“…To realize arbitrary quantum gates, they are decomposed to a set of physically implementable gates by quantum technologies, which is called quantum logic synthesis [19], [20], [21], [22]. This set of gates typically consists of CNOT and single-qubit gates, called "basic gate" library [23] or CNOT and single-qubit rotation gates, called "elementary gate" library [24].…”

An Evolutionary Approach to Optimizing Teleportation Cost in Distributed Quantum Computation

“…The adjacent gates which act on independent subsets of qubits can be applied in parallel and their overall net effect is computed by their tensor product. To realize arbitrary quantum gates, they are decomposed to a set of physically implementable gates by quantum technologies (typically CNOT and single-qubit gates, called"basic gate" library [16]), which is called quantum logic synthesis [17,18,19,20,21,22].…”

An Improved Arbitrated Quantum Scheme with Bell States

“…To realize arbitrary quantum gates, they are decomposed to a set of physically implementable gates by quantum technologies, which is called quantum logic synthesis [19], [20], [21], [22]. This set of gates typically consists of CNOT and single-qubit gates, called "basic gate" library [23] or CNOT and single-qubit rotation gates, called "elementary gate" library [24].…”