Quantum circuit compilers using gate commutation rules

The use of noisy intermediate-scale quantum computers (NISQCs), which consist of dozens of noisy qubits with limited coupling constraints, has been increasing. A circuit compiler, which transforms an input circuit into an equivalent output circuit conforming the coupling constraints with as few additional gates as possible, is essential for running applications on NISQCs. We propose a formulation and two algorithms exploiting gate commutation rules to obtain a better circuit compiler.