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

Circuit depth optimization is crucial for implementing quantum algorithms in practical systems. The decomposition of (n+1)$(n+1)$‐qubit Toffoli gate is continually optimized since this gate is a fundamental component for many quantum algorithms. Without any ancilla, (n+1)$(n+1)$‐qubit Toffoli gate can be decomposed by standard gates with circuit depth 33n−47$33n-47$. Here, the decomposition is further optimized and its circuit depth is reduced to 17n−38$17n-38$. The decomposition is equivalent to (n+1)$(n+1)$‐qubit Toffoli gate up to an overall phase and also does not need any ancilla. [ABSTRACT FROM AUTHOR]