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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 30Day 822

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Year 2·Month 30·Week 2

Day 822: Split Operations & Logical State Preparation

Day 822 of 2,016~20 min read

Learning Objectives

  • •**Define split operations** as the inverse of merge operations
  • •**Analyze the measurement** that occurs during split and its effect on states
  • •**Prepare logical basis states** $|0_L\rangle$, $|1_L\rangle$, $|+_L\rangle$, $|-_L\rangle$ fault-tolerantly
  • •**Design state injection protocols** for arbitrary logical states
  • •**Calculate the resource overhead** for state preparation via lattice surgery
  • •**Implement split operations** in simulation

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Week 118 Lattice Surgery Logical Gates Month 30 Surface CodesSemester 2A Error Correction Year 2 Advanced Quantum ScienceSchedule OverviewLearning Objectives1 Introduction The Split OperationReversing the MergeWhy Split Matters2 Split Operation TheorySetup Merged PatchSplit ProcedureMathematical Effect of Split3 State Projection During SplitInitial Merged StateZZ Split OutcomesComplete Split Protocol4 Logical State PreparationPreparing 0_LranglePreparing _LranglePreparing Arbitrary States5 Fault-Tolerant State PreparationWhy Standard Preparation FailsPost-Selection MethodState Distillation6 Worked ExamplesExample 1 ZZ Split of Bell StateExample 2 Preparing 0_Lrangle via SplitExample 3 Resource Counting for State Preparation7 Practice ProblemsProblem Set A Direct ApplicationProblem Set B IntermediateProblem Set C Challenging8 Computational Lab Split Operations and State Preparation9 SummaryKey Formulas TableKey Takeaways10 Daily Checklist11 Preview Day 823
Day 821Day 822 of 2,016Day 823