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Quantum Engineering Year 2: Advanced Quantum Science Month 35Day 961

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Year 2·Month 35·Week 2

Day 961: First-Order Trotter-Suzuki Formula

Day 961 of 2,016~18 min read

Learning Objectives

•Derive the Lie-Trotter formula from the Baker-Campbell-Hausdorff expansion
•Prove the first-order error bound in terms of commutators
•Compile Trotter steps into quantum circuits for local Hamiltonians
•Calculate the optimal number of Trotter steps for a target precision
•Implement Trotter simulation for the Ising and Heisenberg models
•Analyze the trade-offs between Trotter error and gate count

Today's Schedule (7 hours)

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1 The Lie-Trotter Formula Why Does This Work Historical Context 2 Baker-Campbell-Hausdorff Analysis Accumulated Error Over n Steps 3 Rigorous Error Bounds 4 Extension to Many Terms Error for L Terms 5 Circuit Compilation for Local Hamiltonians Single-Qubit Terms Two-Qubit ZZ Interaction Two-Qubit XX Interaction Two-Qubit YY Interaction 6 Gate Count Analysis Choosing n for Target Precision 7 Ordering Effects and Optimization Randomized Ordering qDRIFT Commuting Groups 8 Connection to Digital vs Analog Simulation

Day 960Day 961 of 2,016Day 962