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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 26Day 718

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Year 2·Month 26·Week 3

Day 718: Subsystem Code Properties

Day 718 of 2,016~16 min read

Learning Objectives

  • •**Define and compute** the distance of a subsystem code
  • •**State the subsystem error correction conditions** (generalized Knill-Laflamme)
  • •**Prove** the relationship between bare/dressed operators and distance
  • •**Apply the singleton bound** to subsystem codes
  • •**Compare** subsystem vs stabilizer code parameters
  • •**Explain** the gauge-distance trade-off

Today's Schedule (7 hours)

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On this page

1 Distance in Subsystem CodesRevisiting the DefinitionBare vs Dressed Distance2 Subsystem Error Correction ConditionsGeneralized Knill-Laflamme ConditionsComparison to Stabilizer CodesSyndrome-Based Condition3 Proof of Error Correction CapabilityTheorem Distance Implies Correction4 The Singleton Bound for Subsystem CodesStatementProof SketchImplications5 The Gauge-Distance Trade-offThe Fundamental Trade-offExample Bacon-Shor Family6 Comparison Subsystem vs Stabilizer CodesParameter ComparisonWhen to Use EachThe No Free Lunch Principle7 Error Detection vs CorrectionDetection DistanceAsymmetric Error Handling
Day 717Day 718 of 2,016Day 719