Towards a generic compilation approach for quantum circuits through resynthesis

In this paper, we propose a generic quantum circuit resynthesis approach for compilation. We use an intermediate representation consisting of Paulistrings over {Z, I} and {X, I} called a ``mixed ZX-phase polynomial``. From this universal representation, we generate a completely new circuit such that all multi-qubit gates (CNOTs) are satisfying a given quantum architecture. Moreover, we attempt to minimize the amount of generated gates. The proposed algorithms generate fewer CNOTs than similar previous methods on different connectivity graphs ranging from 5-20 qubits. In most cases, the CNOT counts are also lower than Qiskit's. For large circuits, containing >= 100 Paulistrings, our proposed algorithms even generate fewer CNOTs than the TKET compiler. Additionally, we give insight into the trade-off between compilation time and final CNOT count.