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Quantum Engineering Year 2: Advanced Quantum Science Month 28Day 768

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Year 2·Month 28·Week 2

Day 768: Threshold Computation Methods

Day 768 of 2,016~16 min read

Learning Objectives

•**Implement** Monte Carlo threshold simulations
•**Apply** tensor network methods for exact threshold bounds
•**Use** statistical mechanics mappings for analytical estimates
•**Analyze** finite-size effects in threshold estimation
•**Compare** different numerical approaches
•**Derive** analytical upper and lower bounds on thresholds

Today's Schedule (7 hours)

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1 Monte Carlo Threshold Simulation Basic Algorithm Error Bars and Statistics Variance Reduction Techniques 2 Finite-Size Scaling Analysis Crossing Method Scaling Collapse Corrections to Scaling 3 Tensor Network Methods Matrix Product State Decoding Approximate Contracted Networks MERA for Hierarchical Codes 4 Statistical Mechanics Approaches Series Expansion Replica Method Cavity Method 5 Analytical Bounds Upper Bounds Achievability Lower Bounds Converse 6 Decoder-Specific Methods MWPM Threshold Union-Find Threshold

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