| name | color-code-pipe-diagrams |
| description | Lattice surgery compilation methodology for color codes using pipe diagrams — extends surface-code pipe diagram framework to triangular color codes on 6.6.6 lattice. Enables distance-independent spacetime optimization, correlation surface realization, and automated compilation to syndrome extraction circuits. |
| license | Complete terms in LICENSE.txt |
| metadata | {"arxiv_id":"2607.05501","published":"2026-07-06","authors":"Laura S. Herzog, Gilad Kishony, Robert Wille, Austin Fowler","tags":["quantum","qec","lattice-surgery","color-code","pipe-diagram","compilation"]} |
Color Code Pipe Diagrams
Description
Extends pipe diagram lattice surgery compilation from surface codes to triangular color codes on 6.6.6 lattice. Color codes offer reduced qubit overhead and transversal single-qubit Clifford gates vs surface codes, but lacked analogous spacetime optimization framework. Provides foundation for automated lattice surgery compilation and diagrammatic optimization in color code FTQC architectures.
Activation Keywords
- color code pipe diagrams
- lattice surgery color code
- color code compilation
- 6.6.6 lattice
- color code spacetime optimization
- pipe diagram quantum
- ZX diagram color code
- 彩色码管道图
Core Concepts
Why Color Codes vs Surface Codes
| Property | Surface Code | Color Code (6.6.6) |
|---|
| Qubit overhead | Higher | Lower |
| Transversal Cliffords | Limited | Full set |
| Lattice surgery framework | Established (pipe diagrams) | This paper |
| Spacetime optimization | Mature | New contribution |
Pipe Diagram Framework for Color Codes
- Representation: Map triangular color code on 6.6.6 lattice to pipe diagrams
- ZX correspondence: Establish correspondence between color code pipes and ZX-diagrammatic computation
- Distance-independent constructions: Correlation surfaces, stabilizers, syndrome extraction circuits
- Compact spacetime embeddings: Leverage color code geometry for efficient logical computation layouts
Key Results (arXiv:2607.05501)
- First pipe diagram representation for triangular color code on 6.6.6 lattice
- Distance-independent constructions of correlation surfaces and stabilizers
- Explicit syndrome extraction circuit realizations
- Demonstrated potential for compact spacetime embeddings
- Foundation for automated color code lattice surgery compilation
Instructions for Agents
Step 1: Problem Selection
- Identify if target QEC code is surface code or color code
- For color codes, use pipe diagram framework (not surface code pipe diagrams)
- Assess qubit overhead tradeoff: color codes use fewer physical qubits per logical
Step 2: Pipe Diagram Construction
- Map color code lattice (6.6.6) to pipe representation
- Establish ZX-diagrammatic correspondence for logical operations
- Construct distance-independent pipe diagrams for target computation
Step 3: Spacetime Optimization
- Design compact spacetime embeddings using color code geometry
- Optimize correlation surface layouts
- Compile to executable syndrome extraction circuits
Step 4: Verification
- Verify correlation surfaces match expected logical behavior
- Check stabilizer measurement patterns
- Validate syndrome extraction circuit correctness
Error Handling
- No established framework for target code: Surface code pipe diagrams ≠ color code pipe diagrams — different lattice geometry requires different constructions
- ZX-diagram mismatch: Color code ZX correspondence differs from surface code; verify mapping before optimization
Related Skills
- lattice-surgery-surface-code — Surface code lattice surgery (different code, different pipe diagrams)
- distributed-quantum-error-correction — Distributed QEC patterns
- quantum-fault-tolerance-benchmark — QEC benchmarking
