Decompositions of n-qubit Toffoli Gates with Linear Circuit Complexity - He, Yong; Luo, Ming-Xing; Zhang, E.; Wang, Hong-Ke; Wang, Xiao-Feng (International journal of theoretical physics, 2017)
Toffoli gates are natural elements for the circuit model based quantum computation. We investigate general resource requirements for arbitrary n -qubit Toffoli gate. These resources consist of the nontrivial Clifford gate (CNOT), non-Clifford gate ( T gate), ancillary qubits, and circuit depth. To implement n -qubit Toffoli gates, we consider two cases: only one auxiliary qubit and unlimited auxiliary qubits. The key of the first case is to decompose an n -qubit Toffoli gate into the reduced Toffoli gate modulo phase shift using the Clifford gates and one ancillary qubit. With this construction, it only requires O ( n ) number of general resources for an n -qubit Toffoli gate. For the second case, an approximate Toffoli gate is constructed to obtain efficient decomposition of a Toffoli gate. The new decomposition can further reduce general resources except auxiliary qubits.