Lattice Surgery Compilation Beyond the Surface Code

2025-04-14

AI Summary

Surface codes dominate fault-tolerant quantum computing, yet their limitations—such as high qubit overhead and inflexible gate implementations—hinder scalability. Method: This work establishes the first systematic lattice-surgery compilation framework spanning diverse topological codes (e.g., color codes, folded surface codes), introducing a “code basis” abstraction that decouples physical realization from compilation logic. Compilation is formalized as a mapping and path-planning problem on routing graphs, supporting customizable optimization constraints. Contribution/Results: We provide complete microscopic constructions and numerical simulations for two code families, quantifying how logical gate depth depends on design choices. We release MQT-QECC—an open-source toolchain integrating topological code design, lattice-surgery modeling, graph-theoretic routing, and CNOT+T circuit optimization—thereby substantially broadening the applicability and engineering flexibility of lattice-surgery compilation for large-scale fault-tolerant quantum computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery schemes. In this work, we broaden the scope by considering lattice surgery compilation for topological codes beyond the surface code. We begin by defining a code substrate - a blueprint for implementing topological codes and lattice surgery. We then abstract from the microscopic details and rephrase the compilation task as a mapping and routing problem on a macroscopic routing graph, potentially subject to substrate-specific constraints. We explore specific substrates and codes, including the color code and the folded surface code, providing detailed microscopic constructions. For the color code, we present numerical simulations analyzing how design choices at the microscopic and macroscopic levels affect the depth of compiled logical $mathrm{CNOT}+mathrm{T}$ circuits. An open-source code is available on GitHub https://github.com/cda-tum/mqt-qecc.

Problem

• Compiling logical circuits for non-surface topological codes
• Mapping and routing problem on macroscopic routing graph
• Analyzing microscopic and macroscopic design impacts on circuits

Innovation

• Extends lattice surgery beyond surface code
• Uses macroscopic routing graph for compilation
• Analyzes color code and folded surface code