  The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318
(2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify
this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$
additional single-qubit gates. The circuit depth is unchanged and no ancilla is
needed. We explicitly show that the circuit after decomposition can be easily
constructed in present physical systems.
