Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice
Kou Hamada, Yasunari Suzuki, Yuuki Tokunaga
TL;DR
This work tackles the challenge of efficiently scheduling lattice-surgery instructions for fault-tolerant quantum computing by reframing the problem as 3D path embedding and routing. It introduces a suite of 3D-path–based scheduling algorithms, most notably the look-ahead Dijkstra projection, which splits long lattice-surgery sequences into smaller fragments and packs their 3D paths to maximize parallelism. Empirical results show up to a 3.8x throughput improvement on SELECT-based benchmarks with modest compilation-time overhead, illustrating a practical path toward high-performance FTQC. The study also establishes a formal link between lattice-surgery scheduling and graph-search problems, extends the approach to many-body lattice surgery, and outlines a full-stack FTQC compilation framework for future integration and scalability.
Abstract
Encoding logical qubits with surface codes and performing multi-qubit logical operations with lattice surgery is one of the most promising approaches to demonstrate fault-tolerant quantum computing. Thus, a method to efficiently schedule a sequence of lattice-surgery operations is vital for high-performance fault-tolerant quantum computing. A possible strategy to improve the throughput of lattice-surgery operations is splitting a large instruction into several small instructions such as Bell state preparation and measurements and executing a part of them in advance. However, scheduling methods to fully utilize this idea have yet to be explored. In this paper, we propose a fast and high-performance scheduling algorithm for lattice-surgery instructions leveraging this strategy. We achieved this by converting the scheduling problem of lattice-surgery instructions to a graph problem of embedding 3D paths into a 3D lattice, which enables us to explore efficient scheduling by solving path search problems in the 3D lattice. Based on this reduction, we propose a method to solve the path-finding problems, look-ahead Dijkstra projection. We numerically show that this method reduced the execution time of benchmark programs generated from quantum phase estimation algorithms by 3.8 times compared with a naive method based on greedy algorithms. Our study establishes the relation between the lattice-surgery scheduling and graph search problems, which leads to further theoretical analysis on compiler optimization of fault-tolerant quantum computing.