color-code-pipe-diagrams

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

1. Representation: Map triangular color code on 6.6.6 lattice to pipe diagrams
2. ZX correspondence: Establish correspondence between color code pipes and ZX-diagrammatic computation
3. Distance-independent constructions: Correlation surfaces, stabilizers, syndrome extraction circuits
4. 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

1. Map color code lattice (6.6.6) to pipe representation
2. Establish ZX-diagrammatic correspondence for logical operations
3. Construct distance-independent pipe diagrams for target computation

Step 3: Spacetime Optimization

1. Design compact spacetime embeddings using color code geometry
2. Optimize correlation surface layouts
3. 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