Linear Decomposition of Approximate Multi-Controlled Single Qubit Gates

We provide a method for compiling approximate multi-controlled single qubit gates into quantum circuits. Without ancilla qubits, the total number of elementary gates to decompose an n-qubit multi-controlled gate is proportional to 32n elementary operations. The proposed decomposition depends on an optimization technique that minimizes the CNOT gate count for multi-target and multi-controlled CNOT and SU(2) gates. We also provide an approximate decomposition with ancilla qubits with lower circuit complexity. Computational experiments show the reduction of CNOT gates when multi-controlled U(2) gates are applied. As multi-controlled single-qubit gates serve as fundamental components of quantum algorithms, the proposed decomposition offers a comprehensive solution that can significantly decrease the count of elementary operations employed in quantum computing applications.