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Quantum Engineering Year 2: Advanced Quantum Science Month 29Day 808

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Year 2·Month 29·Week 4

Day 808: Logical Error Rate Scaling

Day 808 of 2,016~15 min read

Learning Objectives

•Derive the logical error rate scaling formula below threshold
•Distinguish phenomenological from circuit-level noise models
•Calculate threshold values for different noise models
•Analyze qubit overhead for target logical error rates
•Compare surface codes to concatenated codes
•Optimize code distance for given physical error rates
•Perform threshold simulations numerically

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The Fundamental Scaling Law Why d12 Threshold Definition Noise Models and Thresholds Code Capacity Model Phenomenological Model Circuit-Level Model Threshold Comparison Table Resource Overhead Analysis Qubit Overhead Example Calculation Overhead Scaling Table Space-Time Tradeoff Comparison with Other Approaches Surface Code vs Concatenated Codes Break-Even Analysis

Day 807Day 808 of 2,016Day 809