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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 29Day 804

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Year 2·Month 29·Week 3

Day 804: The Rotated Surface Code

Day 804 of 2,016~19 min read

Learning Objectives

  • •**Explain** the geometric transformation that creates the rotated surface code
  • •**Derive** the qubit count reduction: $n = (d^2 + 1)/2$ for data qubits
  • •**Construct** the stabilizer layout for rotated codes
  • •**Compare** rotated and unrotated codes for different metrics
  • •**Describe** hardware-native layouts (heavy-hex, square-octagon)
  • •**Evaluate** tradeoffs between different surface code variants

Today's Schedule (7 hours)

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On this page

Month 29 Topological Codes Week 115 Surface Code ImplementationYear 2 Advanced Quantum ScienceSchedule OverviewLearning ObjectivesMorning Session The 45-Degree Rotation 3 hours1 Motivation for RotationThe Key Insight2 The Rotation TransformationGeometric Picture3 Qubit Count FormulaDerivation4 Comparison Table5 Stabilizer StructureWeight-4 Bulk StabilizersWeight-2 Boundary Stabilizers6 Logical Operators in Rotated CodeQuantum Mechanics ConnectionWhy Rotation HelpsThreshold ImplicationsMapping to HardwareAfternoon Session Hardware Implementations 25 hours1 The Heavy-Hex LatticeHeavy-Hex StructureAdapting Surface Code to Heavy-Hex2 The Square-Octagon Lattice3 Googles Sycamore LayoutSycamore Structure4 Qubit Mapping StrategiesCheckerboard AssignmentSyndrome Extraction Parallelism5 Worked Example Distance-5 Rotated Code on 25 QubitsPractice ProblemsProblem Set 804Direct ApplicationIntermediateChallengingEvening Session Computational Lab 15 hoursLab 804 Rotated Surface Code ConstructionExpected OutputSummaryKey FormulasKey TakeawaysDaily ChecklistPreview Day 805References
Day 803Day 804 of 2,016Day 805