`SurfaceCode`

definition

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module: IndisputableMonolith.Information.QuantumErrorCorrection
domain: Information
line: 195 · github
papers citing: none yet

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IndisputableMonolith.Information.QuantumErrorCorrection on GitHub at line 195.

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depends on

formal source

 192    - Error correction via matching
 193
 194    In RS: The 2D structure relates to holographic boundary. -/
 195structure SurfaceCode where
 196  /-- Lattice size -/
 197  L : ℕ
 198  /-- Number of physical qubits: ~L² -/
 199  n_physical : ℕ := L * L
 200  /-- Number of logical qubits: 1 for simple surface code -/
 201  n_logical : ℕ := 1
 202  /-- Distance: L -/
 203  distance : ℕ := L
 204
 205/-- Surface code threshold: p_threshold ≈ 1%.
 206
 207    Below this error rate, arbitrarily long computation is possible.
 208    Above it, errors accumulate faster than correction. -/
 209noncomputable def surfaceCodeThreshold : ℝ := 0.01
 210
 211/-! ## RS Predictions -/
 212
 213/-- RS predictions for quantum error correction:
 214
 215    1. **8-tick codes**: Natural codes from phase structure
 216    2. **Threshold from τ₀**: Error threshold related to τ₀ timescale
 217    3. **Holographic codes**: Surface codes from holographic boundary
 218    4. **Optimal codes**: Approach may reveal optimal QEC constructions -/
 219def rsPredictions : List String := [
 220  "8-tick structure provides natural encoding",
 221  "Error threshold related to τ₀/gate_time ratio",
 222  "Holographic error correction from ledger projection",
 223  "Novel code families from φ-geometry"
 224]
 225

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