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Quantum Engineering Year 2: Advanced Quantum Science Month 34Day 933

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Year 2·Month 34·Week 2

Day 933: Majorana Fermions

Day 933 of 2,016~18 min read

Learning Objectives

•**Define Majorana operators** and their algebraic properties
•**Decompose fermion operators** into Majorana operators
•**Solve the Kitaev chain** Hamiltonian exactly
•**Identify topological phases** from the band structure
•**Locate Majorana zero modes** at chain ends in the topological phase
•**Explain topological protection** through energy gap and non-locality

Today's Schedule (7 hours)

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On this page

1 What Are Majorana Fermions The Defining Property Additional Properties 2 From Fermions to Majoranas Physical Interpretation 3 The Kitaev Chain Model The Hamiltonian Rewriting in Majorana Operators 4 Two Limiting Cases Case 1 Trivial Phase mu 0 t Delta 0 Case 2 Topological Phase mu 0 t Delta neq 0 5 Majorana Zero Modes Non-Local Fermion Ground State Degeneracy 6 Phase Diagram Bulk Spectrum Gap Closing 7 Topological Invariant 8 Wavefunctions of Zero Modes Quantum Computing Applications Encoding a Qubit Protection Mechanism Operations Multiple Qubits

Day 932Day 933 of 2,016Day 934