MCT Circuit Decomposition for Two-Dimensional Topological Structures

With the rapid development of the field of quantum computing, quantum computing devices have entered the era of noisy intermediate-scale quantum (NISQ). However, current NISQ quantum computing devices still face the challenge of physical constraints. In order to enable quantum algorithms to be directly executed on quantum computing devices, it is necessary to decompose the advanced quantum gates (such as the MCT gate) in the quantum circuit and map them onto the quantum computing devices. This paper proposes a decomposition method for advanced quantum gates that is aware of the two-dimensional topological structure. Based on the proposed decomposition rules of the MCT gate, this method designs a search algorithm for associated gate pairs that is conducive to subsequent decomposition, and divides the control bits of the MCT gate based on the associated gate pairs, making the division method more adaptable to the topological structure. After the associated gate pairs are inversely decomposed to eliminate redundant gates, the circuit mapping is carried out. The experimental results show that the decomposition method proposed in this paper can reduce the number of basic quantum gates in the quantum circuit, with an average optimization rate of 14.6%; for the benchmark circuits using the decomposition method in this paper, when the routing algorithm is applied for mapping, the number of additional gates required is smaller, with an average optimization rate of 20.6%.