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Quantum Engineering Year 2: Advanced Quantum Science Month 28Day 771

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Year 2·Month 28·Week 3

Day 771: Maximum Likelihood Decoding

Day 771 of 2,016~15 min read

Learning Objectives

•**Formulate** the quantum decoding problem as maximum likelihood estimation
•**Derive** the Bayesian posterior probability for errors given syndromes
•**Explain** the coset structure and error degeneracy in stabilizer codes
•**Analyze** the exponential complexity barrier for exact MLD
•**Implement** exact MLD for small stabilizer codes via brute-force enumeration
•**Compare** MLD performance against sub-optimal decoders as a benchmark

Today's Schedule (7 hours)

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1 The Decoding Problem Formalized 2 Bayesian Formulation of MLD 3 Coset Structure and Degeneracy 4 Optimal Decoding Coset Probability 5 Exponential Complexity Barrier 6 Tensor Network Approach to MLD

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