A Robust Quantum Layout Synthesis Algorithm with a Qubit Mapping Checker*

Layout synthesis in quantum circuits maps the logical qubits of a synthesized circuit onto the physical qubits of a hardware device (coupling graph) and complies with the hardware limitations. Existing studies on the problem usually suffer from intractable formulation complexity and thus prohibitively long runtimes. In this paper, we propose an efficient layout synthesizer by developing a satisfiability modulo theories (SMT)-based qubit mapping checker. The proposed qubit mapping checker can efficiently derive a SWAP- free solution if one exists. If no SWAP-free solution exists for a circuit, we propose a divide-and-conquer scheme that utilizes the checker to find SWAP-free sub-solutions for sub-circuits, and the overall solution is found by merging sub-solutions with SWAP insertion. Experimental results show that the proposed optimization flow can achieve more than 3000X runtime speedup over a state- of-the-art work to derive optimal solutions for a set of SWAP-free circuits. Moreover, for the other set of benchmark circuits requiring SWAP gates, our flow achieves more than 800X speedup and obtains near-optimal solutions with only 3% SWAP overhead.