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Quantum Engineering Year 2: Advanced Quantum Science Month 26Day 720

This content was created with AI assistance and may contain errors or inaccuracies. Always verify against authoritative academic sources.

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Year 2·Month 26·Week 3

Day 720: Subsystem Codes and Fault Tolerance

Day 720 of 2,016~18 min read

Learning Objectives

•**Design** fault-tolerant syndrome extraction circuits for subsystem codes
•**Identify** transversal gates on Bacon-Shor and other subsystem codes
•**Explain** gauge fixing and its role in universal computation
•**Analyze** the fault-tolerance threshold for subsystem codes
•**Compare** fault-tolerant protocols for stabilizer vs subsystem codes
•**Construct** complete fault-tolerant gadgets for subsystem codes

Today's Schedule (7 hours)

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On this page

1 Fault-Tolerant Syndrome Extraction The Fault-Tolerance Criterion Natural Fault Tolerance of Gauge Measurements Complete Syndrome Extraction Protocol 2 Fault-Tolerant Gadgets Definition of Gadgets Syndrome Extraction Gadget EC Gadget Gate Gadgets 3 Transversal Gates on Subsystem Codes Transversal Operations Transversal Gates Available Proof Transversal Hadamard on Square Bacon-Shor 4 Gauge Fixing for Computation The Gauge-Fixing Operation Gauge Fixing Protocol Example T-Gate via Gauge Fixing 5 Fault-Tolerance Threshold Threshold Theorem for Subsystem Codes Threshold Estimates Threshold Derivation Sketch 6 Comparison Stabilizer vs Subsystem Fault Tolerance Protocol Comparison When Subsystem Codes Win When Stabilizer Codes Win 7 Universal Fault-Tolerant Computation Gate Set Requirements Bacon-Shor Clifford Gates Non-Clifford Gates

Day 719Day 720 of 2,016Day 721