Circuit Decomposition of Multicontrolled Special Unitary Single-Qubit Gates

Multicontrolled unitary gates have been a subject of interest in quantum computing since their conception and are widely used in quantum algorithms. The current state-of-the-art approach to implementing
$n$
-qubit multicontrolled gates with a single target without relying on auxiliary qubits or approximate results involves the use of a quadratic number of single-qubit and CNOT gates. However, linear solutions are possible for the case where the controlled gate is special unitary, SU(2). The decomposition of an
$n$
-qubit multicontrolled SU(2) gate requires a circuit with a number of CNOT gates proportional to
$28n$
. In this work, we present a new decomposition of
$n$
-qubit multicontrolled SU(2) gates that require a circuit with a number of CNOT gates proportional to
$20n$
and proportional to
$16n$
if the SU(2) gate has at least one real-valued diagonal. The proposed algorithms produce the most efficient known circuits and improve the existing algorithm by reducing the number of CNOT gates and the overall circuit depth. As an application, we show the use of this decomposition for sparse quantum state preparation. Our results are further validated by demonstrating a proof of principle on a quantum device accessed through quantum cloud services.