CNOT gate optimizations via qubit permutations for IBM's quantum architectures

Abstract

IBM offers a number of quantum processors on which scientist can perform experiments. All single qubit gates from the Clifford+T gate library are implemented, but only a subset of the possible CNOT are provided. It is well known that the functionally of the missing gates can be obtained with a sequence of gates. The sequence of gates is based on SWAP gates. Up to seven elementary gates are required to implement a SWAP gate. In this paper we show how the same effect can be achieved with fewer gates. Then, we propose an approach to find all the possible mappings for the missing CNOT gates. IBM's QX5 is used as target architecture. The proposed approach was compared to an algorithm that maps quantum circuits to IBM architectures. The benchmarks without optimizations techniques showed that our approach found circuits with up to 50% fewer gates and with up to 47% fewer levels. To optimize the benchmark circuits the quantum computing framework Qiskit was used. Comparing the optimized mapped circuits, our approach found circuits with up to 50% fewer gates and with up to 49% fewer levels.