TopoLS: Lattice Surgery Compilation via Topological Program Transformations

Abstract: Fault-tolerant quantum computing with surface codes can be achieved by compiling logical circuits into lattice-surgery instructions. To minimize space-time volume, we present TopoLS, a topological compiler that combines ZX-diagram optimizations with Monte Carlo tree search guided by different operation placements and topology-aware circuit partitioning. Our approach enables scalable exploration of lattice surgery structures and consistently reduces resource overhead. Evaluations of various benchmark algorithms across multiple architectures show that TopoLS achieves an average 33% reduction in space-time volume over prior heuristic-based compilers, while maintaining linear compilation time scaling. Compared to the SAT-solver-based compiler, which provides optimal results only for small circuits before becoming intractable, TopoLS offers an effective and scalable solution for lattice-surgery compilation.