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Quantum Engineering Year 2: Advanced Quantum Science Month 34Day 935

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Year 2·Month 34·Week 2

Day 935: Braiding Operations

Day 935 of 2,016~20 min read

Learning Objectives

•**Derive braiding matrices** for Majorana zero modes
•**Compute the effect of braiding** on encoded quantum states
•**Identify the gate set** achievable through Majorana braiding
•**Explain why Ising anyons** produce only Clifford gates
•**Compare Fibonacci anyons** which enable universal computation
•**Design braiding protocols** for specific quantum gates

Today's Schedule (7 hours)

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On this page

1 Braiding Majorana Zero Modes The Exchange Operator Transformation of Majoranas 2 Four Majoranas One Qubit Qubit Encoding Matrix Representation 3 Braiding Matrices in Computational Basis Exchange gamma_1 leftrightarrow gamma_2 Exchange gamma_2 leftrightarrow gamma_3 Exchange gamma_3 leftrightarrow gamma_4 4 The Gate Set from Braiding Important Braiding Products The Clifford Group 5 Why Not Universal The Gottesman-Knill Theorem Topological Reason 6 Fibonacci Anyons Universal Braiding Fibonacci Fusion Rules The Fibonacci Braiding Matrix Universality Proof Sketch 7 Braiding Protocols T-Junction Geometry Measurement-Based Braiding 8 Towards Universality with Majoranas Option 1 Magic State Injection Option 2 Hybrid Systems Option 3 Topological Code Quantum Computing Applications Clifford Gate Compilation Multi-Qubit Gates Error Protection

Day 934Day 935 of 2,016Day 936