Satisfiability Modulo Theories-Based Qubit Mapping for Trapped-Ion Quantum Computing Systems

Qubit mapping is crucial in optimizing the performance of quantum algorithms for physical executions on quantum computing architectures. Many qubit mapping algorithms have been proposed for superconducting systems recently. However, due to their limitations on the physical qubit connectivity, costly SWAP gates are often required to swap logical qubits for proper quantum operations. Trapped-ion systems have emerged as an alternative quantum computing architecture and have gained much recent attention due to their relatively long coherence time, high-fidelity gates, and good scalability for multi-qubit coupling. However, the qubit mapping of the new trapped-ion systems remains a relatively untouched research problem. This paper proposes a new coupling constraint graph with multi-pin nets to model the unique constraints and connectivity patterns in one-dimensional trapped-ion systems. To minimize the time steps for quantum circuit execution satisfying the coupling constraints for trapped-ion systems, we devise a divide-and-conquer solution using Satisfiability Modulo Theories for efficient qubit mapping on trapped-ion quantum computing architectures. Experimental results demonstrate the superiority of our approach in scalability and effectiveness compared to the previous work.