A Decomposition Method of MCT Gates for Reducing Overall Circuit T-depth

It is considered to be very important to reduce so-called the T-depth of a target quantum circuit for realizing future fault-tolerant quantum computation. Thus, there have been many researches to consider how to decompose Multiple Controlled Toffoli (MCT) gates with few T-depth; these existing methods do not consider the T-depth of each qubit when they decompose one MCT gate. In contrast to existing methods, this paper proposes to consider the T-depth of each qubit when we decompose an MCT gate; we show that we can decrease the T-depth by considering the T-depth of each qubit and appropriately selecting ancilla qubits and decomposition methods. In addition, to consider the impact of the decomposition of one MCT gate on the decomposition of subsequent gates, our method utilizes beam search to select a possibly best decomposition for each MCT gate. We confirmed that the proposed method can reduce the T-depth by an average of 17.1% compared to existing methods.