Efficient Realization of Toffoli and NCV Circuits for IBM QX Architectures

Abstract

The quantum computers available from IBM's QX project, implement circuits with Clifford+T gates. In order to implement Toffoli or NCV circuits in such architectures, they need to be mapped to Clifford+T gates. Another challenge is that some CNOT gates cannot be directly implemented in the IBM quantum computers and must be changed to comply with the specific architecture constrains. In this paper we propose a methodology to map Toffoli and NCV circuits such that they are compliant with a given IBM architecture. The proposed approach to accomplish this, is to find a set of low cost mappings for NCV and Toffoli circuits targeting IBM's architecture constraints. With this approach, the number of CNOT that need to be changed will be reduced, resulting in a smaller circuit regarding the number of gates. To evaluate the proposed approach, Toffoli circuits were mapped to Clifford+T and then realized on IBM's QX4 architecture. The benchmarks were compared with Toffoli circuits mapped without the methodology proposed in this paper and implemented on IBM QX4 using two different approaches. The results show that the proposed approach resulted in circuits with up to 67% fewer gates compared with Qiskit and with up to 50% fewer gates compared to a Clifford+T mapping algorithm.