TopoLS: Lattice Surgery Compilation via Topological Program Transformations

TL;DR

This paper addresses the high resource overhead of fault-tolerant quantum computation using lattice surgery on the surface code. It introduces TopoLS, a topology-centric compiler that fuses ZX-calculus optimizations with Monte Carlo Tree Search to optimize merge–split scheduling and 3D embeddings, guided by topology-aware partitioning for scalability. Empirical results show substantial reductions in space–time volume (average around $33\%$) across diverse benchmarks and hardware layouts, with linear compilation-time scaling and strong scalability up to $100$ qubits. The work demonstrates that exploiting the topological nature of lattice surgery yields practical, scalable improvements over gate-centric and SAT-based approaches, facilitating more efficient fault-tolerant quantum computation.

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.

Figures (17)

• Figure 1: Overview of TopoLS workflow
• Figure 2: Logical qubit and patch abstraction
• Figure 3: Lattice surgery and pipe diagram
• Figure 4: ZX-calculus examples
• Figure 5: Overview of Monte Carlo tree search