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Quantum Engineering Year 1: Quantum Mechanics Core Month 21Day 566

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Year 1·Month 21·Week 1

Day 566: Gate Decomposition

Day 566 of 2,016~15 min read

Learning Objectives

•**Decompose any single-qubit gate** using ZYZ Euler angles
•**Derive the decomposition formulas** from matrix elements
•**Understand gate universality** and approximation theorems
•**Implement the Solovay-Kitaev algorithm** conceptually
•**Compile gates** to hardware-native instruction sets
•**Analyze decomposition efficiency** and gate counts

Today's Schedule (7 hours)

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On this page

1 The Decomposition Problem 2 ZYZ Euler Decomposition 3 Extracting Euler Angles 4 Alternative Decompositions 5 Decomposition into Discrete Gates 6 Universal Gate Sets 7 The Solovay-Kitaev Algorithm 8 Native Gate Compilation 9 Gate Synthesis Optimization 10 Practical Decomposition Examples Quantum Computing Connection

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