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Quantum Engineering Year 2: Advanced Quantum Science Month 36Day 997

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Year 2·Month 36·Week 3

Day 997: Semester 2A Review - Surface Codes

Day 997 of 2,016~19 min read

Learning Objectives

•**Construct** rotated surface codes with explicit stabilizer assignments
•**Design** lattice surgery protocols for logical CNOT operations
•**Analyze** decoding algorithms and their complexity trade-offs
•**Evaluate** real-time decoding constraints for practical implementations
•**Interpret** experimental results from Google Willow and IBM systems
•**Calculate** logical error rates from physical error rates

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Core Review Content 1 Surface Code Geometry From Toric to Planar Rotated Surface Code Boundary Types 2 Stabilizer Structure Distance-3 Rotated Surface Code Logical Operators 3 Error Correction Cycle Syndrome Extraction Circuit Syndrome Volume 4 Decoding Algorithms Minimum Weight Perfect Matching MWPM Union-Find Decoder Decoder Comparison 5 Lattice Surgery Concept Logical CNOT via Lattice Surgery Resource Cost 6 Threshold and Scaling Threshold Theorem for Surface Codes Error Suppression Factor 7 Experimental Implementations Google SycamoreWillow 2024 IBM EagleCondor Comparison 8 Real-Time Decoding Requirements Timing Budget Hardware Decoders Concept Map Surface Codes Qualifying Exam Practice Problems Problem 1 Surface Code Parameters 20 points Problem 2 Logical Error Rate Calculation 25 points Problem 3 Lattice Surgery Protocol 25 points Problem 4 Decoder Analysis 20 points Problem 5 Experimental Analysis 10 points Computational Review Summary Tables Surface Code Formulas Decoder Comparison Experimental Milestones Self-Assessment Checklist Surface Code Structure Operations Experiments Preview Day 998

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