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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 32Day 870

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Year 2·Month 32·Week 1

Day 870: Steane to Reed-Muller Switching

Day 870 of 2,016~20 min read

Learning Objectives

  • •**Describe** the complete structure of the [[7,1,3]] Steane code including stabilizers and logical operators
  • •**Construct** the [[15,1,3]] Reed-Muller code from punctured RM codes
  • •**Design** fault-tolerant encoding circuits for both codes
  • •**Implement** the Anderson-Duclos-Cianci-Svore switching protocol
  • •**Analyze** error propagation during code switching operations
  • •**Explain** the recent experimental demonstrations of code switching

Today's Schedule (7 hours)

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OverviewScheduleLearning ObjectivesThe Steane Code 713 ReviewCode ConstructionStabilizer GeneratorsLogical OperatorsLogical Basis StatesTransversal Gates on SteaneThe Reed-Muller Code 1513Construction from Punctured RM CodesParameters VerificationTriorthogonal StructureStabilizer Generators for 1513Logical Operators for 1513The Magic Transversal TThe Code Switching ProtocolOverview Steane Reed-MullerKey Insight Transversal CNOT BridgeThe Anderson-Duclos-Cianci-Svore Protocol 2014Circuit DiagramQubit Mapping Steane RMReed-Muller Steane SwitchingThe Reverse ProtocolSymmetry of the ProtocolFault Tolerance AnalysisError SourcesError Propagation During SwitchFault-Tolerant Gadget RequirementsError Threshold AnalysisExperimental Demonstration Quantinuum 2024The ExperimentKey ResultsImplicationsWorked ExamplesExample 1 Constructing the Logical CNOTExample 2 State Transfer via Code SwitchingExample 3 Error During Code SwitchPractice ProblemsLevel 1 Direct ApplicationLevel 2 IntermediateLevel 3 ChallengingComputational LabSummaryKey FormulasMain TakeawaysDaily ChecklistPreview Day 871
Day 869Day 870 of 2,016Day 871