Decomposing (n+1) (n+1) ‐Qubit Toffoli Gate with Shallow Circuit Depth and No Ancilla

Abstract Circuit depth optimization is crucial for implementing quantum algorithms in practical systems. The decomposition of ‐qubit Toffoli gate is continually optimized since this gate is a fundamental component for many quantum algorithms. Without any ancilla, ‐qubit Toffoli gate can be decomposed by standard gates with circuit depth . Here, the decomposition is further optimized and its circuit depth is reduced to . The decomposition is equivalent to ‐qubit Toffoli gate up to an overall phase and also does not need any ancilla.