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Quantum Engineering Year 2: Advanced Quantum Science Month 26Day 715

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Year 2·Month 26·Week 3

Day 715: Introduction to Subsystem Codes

Day 715 of 2,016~13 min read

Learning Objectives

•**Define subsystem codes** and distinguish them from subspace codes
•**Identify gauge qubits** and their role in error correction
•**Explain the gauge group** and its relationship to the stabilizer
•**Construct simple subsystem codes** from examples
•**Recognize the advantages** of gauge degrees of freedom
•**Connect** subsystem codes to the stabilizer formalism

Today's Schedule (7 hours)

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On this page

1 From Subspace Codes to Subsystem Codes Review Subspace Stabilizer Codes The New Idea Subsystem Codes 2 Formal Definition Subsystem Code Parameters Comparison with Stabilizer Codes 3 The Gauge Group Definition Structure of the Gauge Group 4 Gauge Qubits Intuition Formal Definition 5 Error Correction in Subsystem Codes The Key Advantage Syndrome Measurement 6 First Example The 4112 Code Construction Analysis Why Its Useful 7 Relationship to Stabilizer Codes Every Stabilizer Code is a Subsystem Code Gauge Fixing 8 Why Use Subsystem Codes Advantages Disadvantages

Day 714Day 715 of 2,016Day 716