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Quantum Engineering Year 2: Advanced Quantum Science Month 29Day 803

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Year 2·Month 29·Week 3

Day 803: Defects and Holes in the Surface Code

Day 803 of 2,016~20 min read

Learning Objectives

•**Define** twist defects (genons) and explain their topological origin
•**Construct** holes in the surface code lattice as logical qubit storage
•**Describe** how defect braiding implements logical gates
•**Compare** defect-based operations with lattice surgery
•**Calculate** the resource overhead of defect encodings
•**Analyze** the gate sets achievable through defect manipulation

Today's Schedule (7 hours)

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Month 29 Topological Codes Week 115 Surface Code Implementation Year 2 Advanced Quantum Science Schedule Overview Learning Objectives Morning Session Twist Defects and Genons 3 hours 1 Beyond Standard Boundaries What is a Defect 2 Twist Defects Genons Construction The Genon Property Anyonic Condensation at Twist Defects 3 Creating Twist Defects in Hardware 4 Holes as Logical Qubits Creating a Hole Hole Boundaries Logical Operators from Holes 5 Multiple Holes and Encoding Rate Encoding Rate Comparison Quantum Mechanics Connection Non-Abelian Anyons from Defects Braiding Statistics Implications for Quantum Computing Topological Quantum Field Theory Perspective Afternoon Session Defect Braiding and Lattice Surgery 25 hours 1 Braiding Operations Physical Implementation of Braiding Braiding Smooth Holes Braiding Twist Defects 2 Logical Gates from Defects Gates Achievable by Braiding Example Hadamard from Defect Fusion 3 Lattice Surgery An Alternative Basic Idea Lattice Surgery vs Defect Braiding Current Experimental Preference 4 Worked Example Hole Pair Encoding 5 Resource Analysis Space Overhead for Defect Encoding Time Overhead for Braiding Error Accumulation Practice Problems Problem Set 803 Direct Application Intermediate Challenging Evening Session Computational Lab 15 hours Lab 803 Defect Manipulation Simulation Expected Output Summary Key Formulas Key Takeaways Daily Checklist Preview Day 804 References

Day 802Day 803 of 2,016Day 804