Optimality Study of Existing Quantum Computing Layout Synthesis Tools

Layout synthesis, an important step in quantum computing, processes quantum circuits to satisfy device layout constraints. In this paper, we construct QUEKO benchmarks for this problem, which have known optimal depth. We use QUEKO to evaluate the optimality of current layout synthesis tools, including Cirq from Google, Qiskit from IBM, $\mathsf{t}|\mathsf{ket}\rangle$ from Cambridge Quantum Computing, and recent academic work. To our surprise, despite over a decade of research and development by academia and industry on compilation and synthesis for quantum circuits, we are still able to demonstrate large optimality gaps. Even combining the best of all four solutions we evaluated, the gap is still about 4x for circuits with depths suitable for state-of-the-art devices. This suggests substantial room for improvement. Finally, we also prove the NP-completeness of the layout synthesis problem for quantum computing. We have made the QUEKO benchmarks open source.