Towards Lattice Surgery Compilation for the Color Code Using Pipe Diagrams

2026-07-06

AI Summary

Existing color code architectures lack flexible lattice surgery compilation and spatiotemporal optimization methods. This work proposes a unified compilation framework based on pipeline graphs, introducing pipeline graphs into the color code setting for the first time and establishing their correspondence with ZX-diagrams to enable end-to-end compilation from high-level logical computations to low-level executable circuits. The approach employs a code-distance-independent construction strategy that explicitly represents correlated faces, stabilizers, and syndrome extraction circuits, while supporting efficient graph-based optimizations. Experimental results demonstrate that the framework achieves compact spatiotemporal embeddings under the geometric constraints of color codes, laying the foundation for automated compilation in color code architectures.

Abstract

Pipe diagrams have emerged as a powerful framework for flexible lattice surgery compilation and spacetime optimization for the surface code. In contrast, analogous compilation techniques for color code architectures remain largely unexplored, despite the color code's favorable properties, including reduced qubit overhead and transversal single-qubit Clifford gates. In this work, we develop a pipe diagram representation for the triangular color code on the 6.6.6 lattice and establish its correspondence to ZX-diagrammatic descriptions of computation. We present distance-independent constructions of color code pipe diagrams together with explicit realizations of correlation surfaces, stabilizers, and syndrome extraction circuits. This framework enables both macroscopic optimization of logical computations in spacetime and microscopic compilation to executable syndrome extraction circuits. We demonstrate the potential for compact spacetime embeddings with the color code's geometry. These results provide a foundation for automated lattice surgery compilation and diagrammatic optimization in color code architectures.

Problem

• color code
• lattice surgery
• pipe diagrams
• compilation
• quantum error correction

Innovation

• pipe diagrams
• color code
• lattice surgery
• ZX calculus
• syndrome extraction