Spacetime Layout and Logical Compilation of Color Code

Abstract:Fault-tolerant quantum computing requires system-level coordination of logical primitives. Here, we establish a logical compilation framework for the color code, grounded in its topological structure and supporting universal logical operations. Based on its anyon-condensation and domain-wall structure, we introduce a spacetime block-diagram representation capturing logical patches and operations and derive the rules governing block assembly. A correspondence with ZX diagrams further identifies the logical semantics of this representation and enables transformations that preserve the represented computation. Moreover, we develop a code-derived compilation strategy that converts ZX representations of logical computations into valid color-code spacetime layouts. In this strategy, edge-decorated ZX diagrams tailor the logical representation to the color code under the block-assembly constraints, and fusion-region-aware routing exploits semantic equivalence during geometric embedding. We automate the complete logical compilation process and demonstrate successful compilation across a broad range of algorithms. Our work advances color-code architecture from individual primitives to the automated synthesis of logical computations, marking a significant step toward its full-stack quantum computing.

arXiv:2607.28504 [quant-ph]

(or arXiv:2607.28504v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.28504 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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