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Quantum Engineering Year 2: Advanced Quantum Science Month 33Day 908

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Year 2·Month 33·Week 2

Day 908: Two-Qubit Entangling Gates

Day 908 of 2,016~19 min read

Learning Objectives

•**Derive the Molmer-Sorensen gate** Hamiltonian and dynamics
•**Explain geometric phase accumulation** in entangling gates
•**Analyze the Cirac-Zoller gate** mechanism
•**Calculate gate times and fidelities** for two-qubit operations
•**Design optimal gate parameters** for maximum fidelity
•**Compare different entangling gate schemes** and their trade-offs

Today's Schedule (7 hours)

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On this page

1 Introduction to Two-Qubit Gates 2 Ion-Laser Coupling with Motion 3 The Molmer-Sorensen Gate Bichromatic Drive Hamiltonian Eigenstate Structure Phase Space Dynamics Gate Unitary Gate Time Resulting Entanglement 4 Geometric Phase Gate Phase Space Area Spin-Dependent Displacement Disentanglement from Motion 5 The Cirac-Zoller Gate Protocol Cirac-Zoller Hamiltonian Advantages and Disadvantages 6 Light-Shift Gate Mechanism Two-Ion Gate 7 Gate Optimization Error Sources Multi-Mode Considerations Amplitude Modulation Optimal Gate Time 8 Fidelity Considerations Theoretical Fidelity Scaling with Ion Number Quantum Computing Applications Native Gate Set CNOT Decomposition All-to-All Connectivity

Day 907Day 908 of 2,016Day 909