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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 29Day 790

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Year 2·Month 29·Week 1

Day 790: Error Model and Distance

Day 790 of 2,016~17 min read

Learning Objectives

  • •**Describe** X, Z, and Y errors in terms of stabilizer violations
  • •**Visualize** errors as creating pairs of anyonic excitations
  • •**Define** the code distance as minimum non-trivial loop length
  • •**Explain** the error correction process and minimum-weight decoding
  • •**State** the error threshold (~10.9%) for independent noise
  • •**Compare** toric code performance with other quantum codes

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OverviewScheduleLearning ObjectivesCore Theory1 Single-Qubit Errors2 Error Syndromes3 Error Chains4 Homology and Error Equivalence5 Code Distance6 Minimum Weight Perfect Matching MWPM7 Error Threshold8 Relationship to Random Bond Ising ModelQuantum Mechanics ConnectionAnyonic PictureTopological vs Local ProtectionConnection to Fault ToleranceWorked ExamplesExample 1 Syndrome from Z-Error ChainExample 2 Error CorrectionExample 3 Logical Error ProbabilityPractice ProblemsLevel 1 Direct ApplicationLevel 2 IntermediateLevel 3 ChallengingComputational LabSummaryKey FormulasMain TakeawaysDaily ChecklistPreview Day 791
Day 789Day 790 of 2,016Day 791