A Comparison of Quantum Compilers using a DAG-based or phase polynomial-based Intermediate Representation

In the NISQ era, where quantum computing is dominated by hybrid quantum algorithms, it is important for quantum circuits to be well-optimized to reduce noise from unnecessary gates. We investigate different phase polynomial-based compilation strategies to determine the current best practices and compare them against the DAG-based Qiskit and TKET compilers. We find that phase polynomial-based compiling is very fast compared to DAG-based compiling. For long circuits, these compilers generate fewer CNOT gates than Qiskit or TKET, but for short circuits, they are quite inefficient. We also show that supplementary algorithms such as Reverse Traversal and simulated annealing might improve the generated CNOT count slightly, but the effect is negligable in most settings and generally not worth the additional compiler runtime. Instead, more sophisticated phase polynomial synthesis algorithms are needed.